help-28

[full forum]

@lapis marsh Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[brittle parcel]

I have a technical question regarding factoring 2u^2+5u-18

[brittle parcel]

ok so when factored

it is (u-2)(2u+9)

but I don't see the logic behind it

because 2u^2+5u-18 = 2u^2+9u-4u-18

but shouldn't 9u-4u be something like 9u-2u

because it has to be 18 when multiplied and when added 5

I'm not understanding this

I've always worked in a way that satisfies both situations when multiplied and when added

9*4 is 36

[hot herald]

your quadratic isn't monic

you want to look for a pair of numbers that multiply to ac = 2 * -18 = -36
and sum to 5

[brittle parcel]

Ohh I see

yeah because the original polynomial is 2x^2+5xy-18y^2

but they really never mentioned anything else

I am RANDOMLY supposed to know this information

nowhere in my textbook

no in my lessons

this educational system, man

tysm

.close

[full forum]

Channel closed

Closed by @brittle parcel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[livid grove]

Normal curve is infinite, but can I make a formula for just from 0 to... let's say 3^2 (27)? Is it possible limiting a Normal curve?

[livid grove]

The red one I want but the middle to be half of 27.

So I want a finite Normal curve.

I just did not find how to make it.

Well. Nevermind, I just made something else instead that could work.

.close

[full forum]

Channel closed

Closed by @livid grove

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cosmic shoal]

\left(3\left(x+z^4\right)^{-\frac{1}{4}}z^3sin\left(4t+2\right)\right) how to find partial dericate of z

[rugged harbor]

You forgor the $$

[smoky wing]

$\left(3\left(x+z^4\right)^{-\frac{1}{4}}z^3sin\left(4t+2\right)\right)$how to find partial dericate of z

[glossy valve]

Pure

[cosmic shoal]

oh thanks

[sharp vine]

u mean $\frac{\partial }{\partial z}$

[glossy valve]

Modus

[sharp vine]

?

[cosmic shoal]

i got 3sin(4t+2)(-(x+z^4) z^6 + 3z^2(x+z^4)^-1/4

[cosmic shoal]

yes'

[sharp vine]

you can use Wolfram or Symbolab to check

[cosmic shoal]

i did but i dont get how it got that

[sharp vine]

just treating x, t as constants

[cosmic shoal]

yea i did that

[sharp vine]

so in fact you're supposed to find partial of
$$(x+z^4)^{-\frac{1}{4}}z^{3}$$

[glossy valve]

Modus

[cosmic shoal]

yup

the other sin term is just a constant

[sharp vine]

product rule required

[cosmic shoal]

i got this

[cosmic shoal]

yes did that

[sharp vine]

ok let's check

[cosmic shoal]

also quick question

how do i get wolfram to do it

i forgot how i did it

[sharp vine]

,w d/dz (x+z^4)^(-1/4)z^3

[glossy valve]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Modus#7591

[cosmic shoal]

and i got -(x+z^4)^-5/4 z^6 +3z^2(x+z^4)^-1/4

so if i use product rule

[sharp vine]

it looks correct to me

[cosmic shoal]

(x+z^4)^-1/4 3z^2 + z^3 -1/4(x+z^4)^-5/4 (3z^2)

[cosmic shoal]

how do i simplify to the wolfram

[sharp vine]

idk, try factoring common part etc.

partial derivative has been already calculated

[cosmic shoal]

how did they get 2z^6

not sure how they got 2

and i have a negative sign

they dont

i dont see how they r equal honestly

[sharp vine]

,w -(x+z^4)^(-5/4)*z^6+3z^2(x+z^4)^(-1/4)=(3xz^2+2z^6)/(x+z^4)^(5/4)

[glossy valve]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Modus#7591

[sharp vine]

it's easy

just take out (x+z^4)^(-5/4)

move it to denominator and simplify numerator

[cosmic shoal]

how do i get rid of -1/4 and the negative sign

[sharp vine]

notice that:
$$-(x+z^{4})^{-\frac{5}{4}}z^{6}+3z^{2}(x+z^{4})^{-\frac{1}{4}}=$$
$$=(x+z^{4})^{-\frac{5}{4}}\Big(-z^{6}+3z^{2}(x+z^{4})\Big)$$

[glossy valve]

Modus

[sharp vine]

simplify the bracket then you'll see

[cosmic shoal]

how did the -1/4 go away

[sharp vine]

$$(x+z^{4})^{-\frac{5}{4}} \cdot (x+z^{4})^{1}=(x+z^{4})^{-\frac{5}{4}+1}=$$
$$=(x+z^{4})^{-\frac{1}{4}}$$

[glossy valve]

Modus

[cosmic shoal]

thank you so much

[full forum]

@cosmic shoal Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[torn jolt]

I have absolutely no idea what’s going on, I don’t know how to put the two things into the graphing Utility

I don’t even know what I’m looking for the local maximum of

I’m just lost

[light sonnet]

Well, you plot the equation and restrict it to [-2, 2]

Do you know what a minimum is?

[torn jolt]

Yes the smallest thing graphed

Maximum is the largest thing graphed

Or that can be graphed

[light sonnet]

What do you mean "thing"?

[torn jolt]

The lines

I mean points

[light sonnet]

So the minimum is the lowest point of the graph

[torn jolt]

Yes

[light sonnet]

Is that what you're trying to say?

[torn jolt]

Or that can be graphed

Ye

Is that wrong

[light sonnet]

First, did you graph it and restrict the graph to be in between [-2, 2]?

[torn jolt]

Yes

[light sonnet]

What's the lowest point of that restricted graph?

Like the y value

[torn jolt]

It doesn’t show one

[light sonnet]

You use the graph to estimate the value

[torn jolt]

I know

However

There’s nothing there

[light sonnet]

Because you didn't graph the equation

[torn jolt]

I put it in like it shows

[torn jolt]

The lowest point is -2?

[light sonnet]

What's the equation

[torn jolt]

I’m sorry, what equation?

[light sonnet]

The given equation

[torn jolt]

It doesn’t give an equation

[light sonnet]

Yes it does

[torn jolt]

Ok ok

Tell me how to put the graph in

Because what I see there is no equation

[light sonnet]

The equation you need to plot is given to you

Plot it

[torn jolt]

I did

And it gave me a single dot

Between -2,2

[light sonnet]

That's not the equation

An equation has variables, right?

[torn jolt]

Yes

But what you’re not understanding is idk where to get the equation

[light sonnet]

It's given to you

Did you read the question?

[torn jolt]

X^3-2x+5

Jesus

[light sonnet]

Yes, that's the equation

So you need to plot that equation and restrict it between [-2, 2], what should the answer for part a be?

[torn jolt]

Uhh

Idk

How would I do that

And also do I put the equation into the graph

[light sonnet]

Type in the equation

[torn jolt]

Done

[light sonnet]

You can change the x and y scale, in the settings to the given settings it gives

In part a

[torn jolt]

Ok?

What am I looking for exactly

I’m currently trying to figure out which graph is correct before the minimum

[light sonnet]

You need to answer part a, first, right?

[torn jolt]

Yes

Part A is finding the graph

[light sonnet]

So did you find the answer that matches the graph you need?

[torn jolt]

No

[light sonnet]

Out of the 3 given choices, for part A, which one matches the plotted graph on the graph utility?

[torn jolt]

None

[torn jolt]

Comparing this graph

To the ones on the multiple choice it’s not similar

I think we have to find something involving the two graphs here

[light sonnet]

This is the plotted function

[light sonnet]

Does it look like this?

[torn jolt]

No

[light sonnet]

Why would b the answer?

[torn jolt]

I meant to show you all of them

Do you know what you’re doing?

because we haven’t made any progress

[light sonnet]

I know what to do, it seems like you don't

[torn jolt]

Well clearly that’s why I’m here

stating the obvious aren’t we

However I’m asking you how would we find the graphs that would be similar to A,B or C

[light sonnet]

Use this

[torn jolt]

You told me to put the equation in that’s exactly what I did and the end result was a graph

That didn’t look like anything

[light sonnet]

Well, did you change the x and y axis settings?

[torn jolt]

Yes

End result was nothing

[light sonnet]

Then you changed the settings wrong

[torn jolt]

Tell me how to change the setting

[light sonnet]

Literally tells you how to set the scale of the axes in part a

[torn jolt]

Lord have mercy

[light sonnet]

I don't use desmos that often, you can google how to change the axes scale

If you don't know how to

Google can answer a lot of things

[torn jolt]

Oh….

So you were wrong

because I just sat here for maybe an hour with you no progress for you to just tell me

You don’t know how to use what I’m using

Kill me niw

[light sonnet]

Wrong about what? Not being able to solve this? I know how to do it

I use different graphing utilities than you, like an actual physical graphing calculator

[torn jolt]

Then explain

[torn jolt]

I HAVE THAT INFRONT OF ME YOU TWAT

ok

Let’s start over

I opened my graphing calculator now what

[light sonnet]

You are using a website that I barely use. I use an actual graphing calculator

[light sonnet]

Plot the given function, restricted between [-2, 2]

[torn jolt]

Ok

So now what

[torn jolt]

How do I put this into the calculator idk how

I know how to go to the plotting menu

Besides that I’m lost

[light sonnet]

Plot the equation

By typing it in

Then change the window, to match the scale that is given in part A

[torn jolt]

There’s no comma to separate the twos on the capacitor

[light sonnet]

You don't need a comma

[torn jolt]

Ok

[light sonnet]

You plot in the equation, then change the window scale

[torn jolt]

Ok

How do I change the window the scale

[light sonnet]

By clicking the window button and changing the min/max of x and y to match what is given in part A

[torn jolt]

So I’m changing it to 2

[light sonnet]

Cause it gives $-2\leq x \leq 2$

[glossy valve]

dldh06

[light sonnet]

You need to change both the min and max

[torn jolt]

This would have been so much easier

If you had just said this at first

[light sonnet]

Do the same thing for y

[torn jolt]

Already did

Now

What

[light sonnet]

Look at the graph

Out of the 3 options, what does it match, in part A?

[torn jolt]

See

I love you so much

You could be my boyfriend if you weren’t so difficult

So I’m looking for the local maximum?

[light sonnet]

Yes, what is the y value of that local max?

Because the question asks for y first

[torn jolt]

5?

[light sonnet]

Not quite

[torn jolt]

Idk what I’m looking at

However you just taught me how to graph

Meat

[light sonnet]

Do you have the graph? What does it look like?

[light sonnet]

Were you able to answer part A?

[torn jolt]

It was A

[rotund blaze]

Hey

[torn jolt]

Heyyy nova

[rotund blaze]

Csn some help me with my hmw real quick

[torn jolt]

I’m getting help currently nova

Love you babes

[light sonnet]

#❓how-to-get-help

[rotund blaze]

Should i ask here

[torn jolt]

No

[light sonnet]

If you hit the left/right arrows, you should see a cursor and values on the bottom

[rotund blaze]

Oh mb where then

[light sonnet]

Like really? Read #❓how-to-get-help

[torn jolt]

Here

[rotund blaze]

Ok ty

[torn jolt]

Np

Cya later

[torn jolt]

Ok?

It’s 10

[light sonnet]

No?

How about this? Hit the trace button and use that

You can scroll along the graph using that

[torn jolt]

Scrolling until I find what

[light sonnet]

Look at the y value, scroll until you reach the point where the max is, Then determine approximately what that y value is for the max

[light sonnet]

So this plot, the max looks like it's on the left side

Using the trace, scroll all the way to the left, to that max

[torn jolt]

I think it’s infinite

[light sonnet]

When you approach it, it displays a y value at the bottom

Just look at it and see approximately what the y value is

[torn jolt]

9?….

[light sonnet]

The local max

Local max is the highest part of the function, meaning the highest "mountain", right?

[torn jolt]

Sure

Which is 9

[light sonnet]

No, not quite

The highest "mountain", does that part of the graph look like a "mountain"?

[torn jolt]

Yes

[light sonnet]

Are you sure?

[torn jolt]

Is it 10.3?

Anything else is no longer on the graph to where I can see it

[light sonnet]

I mountain looks like this

[light sonnet]

Does this look like a mountain?

That point you are at

[torn jolt]

Lord have mercy

You are so right

6

[light sonnet]

Because you went too far right, it shifted the x scale, you need to reset the x scale, under window again

[light sonnet]

Yes, that is approximately the y value of the max

What is the corresponding x value?

[torn jolt]

.85

[light sonnet]

Also, it says to round to 2 decimal places

[torn jolt]

6.1

[light sonnet]

That is not two decimal places

[torn jolt]

Fight me about it

How do I graph

I mean

6.085

[light sonnet]

Also, to approximately find the proper x value, you want to scroll around that "mountain" and look at the y value, and determine what the highest y is

[torn jolt]

Would be 6.0 what?

[light sonnet]

Like if you hit the right arrow, what is the y value now?

[light sonnet]

Still not 2 decimal places

Two decimal places is two values after the decimal point

[torn jolt]

6. What

Say a answer

[light sonnet]

Look at the y value at the bottom of the calculator

It tells you what the y value is at where the cursor is, you just need to round

[torn jolt]

I see it

However

[light sonnet]

However?

[torn jolt]

6.09

[light sonnet]

Good

What is the corresponding x value with that y value?

[torn jolt]

Uhh

.85

Or do you mean the mountain for the x axis

[light sonnet]

So here is what I was saying, about the scrolling part. The current y value you are at is 6.0856 ish

If you scroll one more to the right, what is the y value now?

And is it bigger or smaller than 6.0856?

[torn jolt]

Bigger?

6.088

But when rounding up

It stays the same

[light sonnet]

Yes that is true, but look at the x value at that point

What is the x value at y = 6.088?

[torn jolt]

.80

[light sonnet]

This here is the proper max

Because if you weren't using the proper max, the x value would have bee different

[light sonnet]

Like here, this was the x value when y = 6.085

[light sonnet]

And here, even though it is rounded wrong, is the x value at y = 6.088

[torn jolt]

Hm

[light sonnet]

Also not the right value either

So looking at where y = 6.0885, what is the x value at that point?

[torn jolt]

Lord have mercy

[light sonnet]

You are looking at y = 6.0885, correct?

[torn jolt]

👍🏿

[light sonnet]

What is the x value?

[torn jolt]

Idk

.80

[light sonnet]

One, sign, two rounded wrong

[torn jolt]

.81

[light sonnet]

The sign is still wrong

[torn jolt]

What sign

[light sonnet]

Is it a positive or negative value?

[torn jolt]

-.81

[light sonnet]

So there you go

That's the local max

Do the same for the min

[torn jolt]

Lord have mercy

[light sonnet]

Process is the same

[torn jolt]

It’s slow

Though

[light sonnet]

You know how to do local max, apply it to local min

[torn jolt]

Wait the min of what

[light sonnet]

The local min

[torn jolt]

With the mountain facing downward

3.9 and .80

[light sonnet]

The x value isn't rounded properly

But yes

[torn jolt]

.81

[light sonnet]

Yes

[torn jolt]

That was easy

Where is it increasing

And deceasing

[light sonnet]

That's where the slope is positive

[torn jolt]

I know

But what’s the answe

[light sonnet]

This is where you use the values min/max values you found

What part(s) looks like it's increasing?

[torn jolt]

I think it’s

[light sonnet]

These are using the x values

So what part is decreasing?

Between what x values?

[torn jolt]

D

It’s D

[light sonnet]

For decreasing?

[torn jolt]

Yes

[light sonnet]

So it decreases at [-2, -0.82] and [0.82, 2]?

[torn jolt]

Yea?

[light sonnet]

Decreasing has a negative slope, does the slope look positive or negative for this?

[torn jolt]

Oh

B

[light sonnet]

Good

What about increases?

[torn jolt]

B again

It’s increasing

[light sonnet]

Good

Not sure what else is after that part

[light sonnet]

That's a new question

[torn jolt]

Yea

[light sonnet]

Well, you used an online solver, those are normally correct

[torn jolt]

Did I put it in correctly is my question

[light sonnet]

It does say round to 2 decimal places

[torn jolt]

I got a 35

I need more help

Help

What do I do for this

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

More help

[torn jolt]

.close

[full forum]

Channel closed

Closed by @chrome kernel

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[elder granite]

Im stuck trying to compute this integral (#22)

[elder granite]

Here is my work

I tried u-sub which led to u/du which I dont know how to further expand, then I tried using basic integration formulas which got me the wrong answer.

<@&286206848099549185>

[gritty rose]

,rotate

[gritty rose]

Why's it wrong

[elder granite]

This is the correct answer, which is not the same as what I computed

I want to know where I went wrong

[gritty rose]

,w integral sec(x)dx

[glossy valve]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by riemann#2529

[gritty rose]

Oh they used some double angle formula

[elder granite]

yeah my precalc is rusty. Not sure what they did exactly

,w integral tan(x)dx

[glossy valve]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Dunkin Duck#9783

[full forum]

@elder granite Has your question been resolved?

[gritty rose]

That part was right. It's the integral of secant that was wrong, maybe.

That should be something you learned or can look up in a table

[elder granite]

I see now.

I only knew it was equal to the middle value

So I guess my answer wasn’t wrong in the first place 😅

[elder granite]

.close

[full forum]

Channel closed

Closed by @elder granite

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rapid atlas]

I am just confused on what to do and how to set it up

[full forum]

@rapid atlas Has your question been resolved?

[full forum]

@rapid atlas Has your question been resolved?

[rapid atlas]

<@&286206848099549185>

Could Somebody please help me with my problem

bro theres no way

after more then an hour

[rapid atlas]

.close

[full forum]

Channel closed

Closed by @rapid atlas

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[young cairn]

Hi!
I got a problem in linear algebra. I have 6 points of an octahedron (+-1, 0, 0), (0, +-1, 0), (0, 0, +-1). Then I have a plane x+y+z = 0. My task is to find the cross section (the points of it) of the octahedron and the plane.

[young cairn]

I mean, you can solve it by drawing a line from each point to 4 of it's nearest points, creating a total of 12 lines

And then see where those lines intersect

But that feels tedious

[brittle steeple]

How good are you at visualizing in 3d?

[young cairn]

I mean, I got it up there

But not sure if it's okay to reason that I've visualized it in my head

[brittle steeple]

Ah

You could try using the equation of the octahedron itself

[young cairn]

How would that equation look?

[brittle steeple]

|x|+|y|+|z|=1 I believe

not sure if that helps really though

[young cairn]

I don't really see how it would help unfortunately

[brittle steeple]

Hmm

Could write out the lines just by listing their endpoints

Instead of calculating the whole equation

Might be less tedious and still give useful information

[young cairn]

How would I do that?

[brittle steeple]

each endpoint connects to every other one except it's opposite

So 1,0,0 connects to every endpoint except -1,0,0

[young cairn]

Yeah, how would I get out the points of the cross section?

[brittle steeple]

Looking at x+y+z of the endpoints

That is adding their coordinates together

If one endpoint has sum of coordinates less than zero and one had sum of coordinates greater than zero

Then somewhere between the two points the line has to hit x+y+z=0 and intersect the plane

If not, then not

[young cairn]

Once I find that, do I then need to create a line between those two points and then find the intersection of the plane?

[brittle steeple]

You can

[young cairn]

Or is there a better way?

[brittle steeple]

However you'll also find in the 6? cases where lines intersect

one endpoint of the line will have sum of coordinates +1

one will have sum of coordinates -1

so the midpoint is the intersection

anyways g2g

[young cairn]

Interesting, alright. Thank you very much

I think I can maybe reason that way

.close

[full forum]

Channel closed

Closed by @young cairn

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vale glacier]

why i is (1,0,0)?

[smoky wing]

i is the unit vector in the x direction

[vale glacier]

how do you know

[sacred fog]

by definition

[vale glacier]

how about y and z-direction

[smoky wing]

j = (0,1,0)

k=(0,0,1)

[vale glacier]

oh ok

noted

[sacred fog]

usually î ĵ ^k

(my mobile keyboard doesn't have k with a hat)

[vale glacier]

.close

[full forum]

Channel closed

Closed by @vale glacier

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[deft zodiac]

in complex ana, when asked for num of soln, they mean zeros counted with multiplicities right

[topaz valley]

depends on how its asked

[topaz valley]

eh

i reckon its with multiplicities

otherwise you cant really say for sure

[deft zodiac]

yes

ty

.close

[full forum]

Channel closed

Closed by @deft zodiac

Use .reopen if this was a mistake.

[topaz valley]

❄️

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Channel closed

Closed due to the original message being deleted

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[modern sentinel]

how can i solve this

[modern sentinel]

proper method pls

[deft zodiac]

i think

u can just throw 120

cuz it has to be >90

thrs only 1 option

if its <= 90 then the option would be >

[modern sentinel]

can u send a proper method, without options

[deft zodiac]

but when u take -b its smaller

[brittle steeple]

are a and b vectors?

[vast fossil]

a*b = -(a^2 + b^2)/4 is the furthest I got to

[deft zodiac]

u can try using trig on this

so with the

we can get |a-b| = sqrt(1 + 1 + 2cos(theta))

repeat for this and find equations

probably a

horrible method

[modern sentinel]

how did u got to that

[modern sentinel]

yea but this is a bit lengthier ...

there must be some proeprties on modulus in vectors

[vast fossil]

Multiply both sides by sqrt3, square both sides and then isolate ab

[deft zodiac]

[modern sentinel]

how do i isolate ab

[vast fossil]

3(a^2 + 2ab + b^2) = a^2 - 2ab + b^2
3(a^2 + b^2) = a^2 + b^2 - 2ab
2(a^2 + b^2) = -8ab
ab = -(a^2 + b^2)/4

[deft zodiac]

let a = (1,0)
let b be theta anticlockwise from a
b = (cos theta, sin theta)

$|a+b| = \frac{|a-b|}{\sqrt{3}}$

[modern sentinel]

i dont think we can do that, they're vectors not just variables

[modern sentinel]

hmm

[vast fossil]

Why not? (a + b)^2 = a^2 + 2ab + b^2 works in vectors too

[modern sentinel]

but isnt it modulus

[vast fossil]

And I mean |a + b|, a^2 and ab are indeed numbers

[vast fossil]

You mean |a + b|^2?

[modern sentinel]

yes

[deft zodiac]

$|a+b| = \sqrt{(1+cos(\theta))^2+sin(\theta)^2}$

[vast fossil]

(a + b)^2 = (a + b) * (a + b) = |a + b|^2

[modern sentinel]

what's
(i+j)^2

[vast fossil]

2

[deft zodiac]

$|a+b| = \sqrt{(1+cos(\theta))^2+sin(\theta)^2}$\\
$= \sqrt{1+cos(\theta)^2+2sin(\theta)cos(\theta)+sin(\theta)^2}$

[modern sentinel]

yea so according to ur method, it should be 1+1+2.1.1=3 which is wrong

[vast fossil]

No, i * j = 0

[deft zodiac]

$|a+b| = \sqrt{(1+cos(\theta))^2+sin(\theta)^2}$\
$= \sqrt{1+cos(\theta)^2+2sin(\theta)cos(\theta)+sin(\theta)^2}$\
$= \sqrt{2+2sin(\theta)cos(\theta)}$

[vast fossil]

(i + j)^2 = i^2 + 2ij + j^2 = 1 + 0 + 1

[modern sentinel]

u shouldve written ab as a.b i got confused, sry

[modern sentinel]

ill try ur method

[deft zodiac]

$\frac{|a-b|}{\sqrt{3}} = \frac{1}{\sqrt{3}}\sqrt{(1-cos(\theta))^2+(-sin(\theta))^2}$
$= \frac{1}{\sqrt{3}}\sqrt{1+cos(\theta)^2-2sin(\theta)cos(\theta)+sin(\theta)^2}$
$= \frac{1}{\sqrt{3}}\sqrt{2-2sin(\theta)cos(\theta)}$

[deft zodiac]

this is pain T.T

$\frac{|a-b|}{\sqrt{3}} = \frac{1}{\sqrt{3}}\sqrt{(1-cos(\theta))^2+(-sin(\theta))^2}$
$= \frac{1}{\sqrt{3}}\sqrt{1+cos(\theta)^2-2sin(\theta)cos(\theta)+sin(\theta)^2}$
$= \frac{1}{\sqrt{3}}\sqrt{2-2sin(\theta)cos(\theta)}$ \\
$= \frac{1}{\sqrt{3}}\sqrt{2-sin(2\theta)}$

[deft zodiac]

$|a+b| = \sqrt{(1+cos(\theta))^2+sin(\theta)^2}$
$= \sqrt{1+cos(\theta)^2+2sin(\theta)cos(\theta)+sin(\theta)^2}$
$= \sqrt{2+2sin(\theta)cos(\theta)}$
$= \sqrt{2+sin(2\theta)}$

[modern sentinel]

i got cos theta=1/2 so angle between themis pi/3 ?

[deft zodiac]

we can square both sides

so

and equate both side to find theta,

[modern sentinel]

oh no wait i got cos tehta=-1/2

so angle would be 2pi/3?

[modern sentinel]

yes i did that

[deft zodiac]

$\frac{2-sin(2\theta)}{3}=2+sin(2\theta)$

[deft zodiac]

na im just

learning latex as i go along haha

[modern sentinel]

okay

[deft zodiac]

$4sin(2\theta) = -4$

[deft zodiac]

yea i got

hm so

$2\theta = \frac{3\pi}{2}$

[deft zodiac]

$\theta = \frac{3\pi}{4} = 135$

[deft zodiac]

OH NOONO

:c

OMG

I DID IT

its

hahhaa

so

we take

[deft zodiac]

hm quite similar to this

ill nab this

$3(a^2 + 2ab + b^2) = a^2 - 2ab + b^2$

[deft zodiac]

but in this case as a and b are unit vectors we have

$a^2$ = 1\\b^2=1\\|ab| = |a||b|cos(\theta) = cos(\theta)$

[glossy valve]

Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[deft zodiac]

so this simplifies to $6+6cos(\theta)=2-2cos(\theta)$

[deft zodiac]

$8cos(\theta)=-4$

[deft zodiac]

$\theta = \frac{\pi}{4}

omg i think i did smt wrong again

well

no its actually

theta = 135 again

!!

what

is the ans 45

nay?

anw im out its been awhile

[full forum]

@modern sentinel Has your question been resolved?

[cloud shore]

Does the hat mean it's a unit vector?

If so, square both sides and use x.x = |x|^2

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[granite elk]

im confused basically what im thinking is 80 = k x 4

[granite elk]

but the square just messes it all up

am i supposed the square the 4

.close

[full forum]

Channel closed

Closed by @granite elk

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[runic bloom]

how do I find the derivative of $\frac{x^5 - 3x^2 + 2}{x^(1/2)}$

[glossy valve]

Kihei

[runic bloom]

oh thats some fucked latex

I haven't learned quotient rule yet btw

so I can't use that

[sharp vine]

divide it firstly

each term of the numerator

then use power rule

[runic bloom]

I was doing that but then what'll I do with 2 / x^1/2

[spice pond]

2 / x^1/2 = 2x^0 / x^1/2

[sharp vine]

$$\frac{2}{x^{\frac{1}{2}}}=2x^{-\frac{1}{2}}$$

[runic bloom]

OHH

[glossy valve]

Modus

[runic bloom]

wow another moment brain.exe has stopped responding

okay one sec

so dividing it got me $x^(\frac{9}{2}) - 3x^(\frac{3}{2}) + 2x^(\frac{-1}{2})$

[glossy valve]

Kihei

[spice pond]

yeah then just use the power rule

[keen spruce]

power rule time

[runic bloom]

yeah so then I got

$(9/2)x^(7/2) - (9/2)x^(1/2) - x^(-3/2)$

[glossy valve]

Kihei

[runic bloom]

is that right?

(wow I really need to figure out latex)

[spice pond]

yeah

[gritty rose]

{} instead of () in exponent

$K^{ihei}$

[glossy valve]

riemann (eric tao for honorable)

[runic bloom]

ohh LOL

[spice pond]

$x^{-3/2}$

[glossy valve]

imagine

[spice pond]

o.o

[runic bloom]

thanks guys

.close

[full forum]

Channel closed

Closed by @runic bloom

Use .reopen if this was a mistake.

[keen spruce]

bye

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[deft zodiac]

whys this wrong

[deft zodiac]

doesnt it go to zero

f approaches 0 and e^(z-c) has taylor expansion of 1+O(x)

f is of O(x)

where x->0

we got

i dont get this as well

similar but theres also this

[brittle steeple]

idk what's up with the other ones

[deft zodiac]

hm?

[brittle steeple]

are these functions on real variables now?

not complex analysis right

[deft zodiac]

C

[brittle steeple]

bruh they don't even have limits

how u gonna have limits as x -> infinity

[deft zodiac]

what are u talking about now

can u not jump from 1 to another

[brittle steeple]

z -> infinity limits

ok actually i can see it ig

[deft zodiac]

yea we are just trying to represent it in landaus notation

[brittle steeple]

ok so just to clarify

z -> infinity means the real part of z goes to infinity while the complex part goes to 0

[deft zodiac]

um

theres only 1 infinity in the complex plane

[brittle steeple]

like it would be |y-L| when Re(z) > N and Im(z) < delta or something

[brittle steeple]

is it just everywhere?

[deft zodiac]

kinda

[brittle steeple]

like when |z| > N

|y-L| has to be less than epsilon?

[deft zodiac]

u can approach inf from any direction

can u like

not drown my q with random stuff

-.-

[brittle steeple]

i thought i saw your mistake on the last problem

i just need to clarify

[deft zodiac]

u didnt even understand inf or landaus o notation

just search up on it first

[brittle steeple]

i know what o notation is for real numbers

didn't know it was called "landau" but

[deft zodiac]

ok nvm i got it

e^z doesnt have a limit at inf

kinda realised that e^z would take on arbitrarily small vals

just forgot about it

but

u rly shouldnt just

nvm

.close

[full forum]

Channel closed

Closed by @deft zodiac

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[noble apex]

i need help understanding the problem and solving it, the teacher hasnt taught us im going ahead

[full forum]

@noble apex Has your question been resolved?

[full forum]

@noble apex Has your question been resolved?

[night folio]

What don't you understand?

[noble apex]

how i am supposed to slove this

i think it want me to find a horizontal line that intsersects the graph at 2 points form 0 to 2pi

but idk how to find that

[night folio]

It wants you to find when both fish are at the same height above the water so -sin(x) = 2cos^2(x) - 1
With the constraint that both sides should be positive i guess

[noble apex]

oh

got it

alr i got it thanks

.close

[full forum]

Channel closed

Closed by @noble apex

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[runic bloom]

idk how to begin

I could simplify that but it doesn't seem to get anywhere

I think

[torn jolt]

This seems to be similar to the limit definition of a derivative?

It also not the same

So idk

[runic bloom]

YEAH I noticed that too

[torn jolt]

Sorry that’s all I can help with

[runic bloom]

the problem was given with h instead of x

[torn jolt]

Yeah

[runic bloom]

I just put it online using x

but yea

hmm

[torn jolt]

It’s probably asking you to take a derivative the

N

Of

Something

[runic bloom]

I checked desmos and the limit is 1/2

[torn jolt]

Interesting

[runic bloom]

and there is indeed 1/2 in the limit expression

hmm perhaps f(x) = 8x^8

but then they substituted 1/2 for x??

why

is it just feeding us the limit

[full forum]

@runic bloom Has your question been resolved?

[full forum]

@runic bloom Has your question been resolved?

[runic bloom]

<@&286206848099549185>

[torn jolt]

Yup you're almost there
Limit definition of derivative of 8x^8 gives you f'(x)=lim_(h->0) [(8(x+h)^8-8x^8)/h]

From there you can let x=1/2 and you get the same limit as you had in the image, just with the variable h instead of x

[runic bloom]

but why did they let x=1/2?

like why that value

[torn jolt]

Well the limit definition of the derivative holds true for all specific values of x

So you can intuit that choosing x=1/2 would be helpful because it sets up an equation that contains the limit you want to find

Which'd be equal to f'(1/2)

Easier to find

[runic bloom]

ohh

so it just happens, that at x=1/2, the derivative is also 1/2

I see now thank you

.close

[full forum]

Channel closed

Closed by @runic bloom

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[modern bobcat]

hi, i was just wondering if anyone could help me understand why they got d/dx (36) from 144?

[atomic blade]

No idea

Doesn't matter anyways lol

[modern bobcat]

well this is the example to replicate for a similar problem so like idk how to do it lol

[atomic blade]

Product rule

[modern bobcat]

ohhh

thank you

[spice pond]

the fuck

yeah it doesnt matter but lmaoo

[atomic blade]

They uh

Did a different perfect square

Said "fuck it, it don't matter"

[modern bobcat]

is it the wrong answer?

[spice pond]

no, it doesn't matter cuz the derivative of a constant is 0 anyway

[modern bobcat]

oh okay i see what you mean

thank you both

[full forum]

@modern bobcat Has your question been resolved?

Channel closed

Closed by @modern bobcat

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vague scarab]

Use Polya's Technique to solve the problem given below. Indicate per steps. ( step 1-2 pts, step 2-3 points, step 3-5pts, step 4-3pts). Upload your answer in the MS Teams.

The International State College of the Philippines (ISCP) opens 1500 slots for freshmen this Academic Year 2022-2023. Each slot should be allotted to one of the following colleges: College of Law, College of Education, College of Arts and Sciences. Programs in College of Law costs 2000 per semester, 1500 for College of Arts and Sciences and 1200 for College of Education. The ISCP cashier determined that the total collection for this semester is 2,675,000. If the number of slots given to the College of Law is twice as the sum of the slots given to the College of Arts and Sciences and College of Education, determine the number of slots given to the three colleges in the ISCP.

[vague scarab]

helpp

<@&286206848099549185>

[light sonnet]

!15m

[full forum]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

@vague scarab Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wide estuary]

What areas are not possible for any acute triangle created on a 5x5 grid

[deft zodiac]

um

the largest space it can take up would be half the grid

so any area >half the 5x5 grid

[wild sleet]

that's a right triangle

[deft zodiac]

it neednt be

[wild sleet]

oh

base times height is area

[deft zodiac]

yes

just pick any l as base

and h can be pick atany except a corner

[wild sleet]

wait but

ok i've no clue

[neat bay]

interesting question

one thing I just thought of

if you have an obtuse or right triangle, you can create an acute triangle with the same area by simply sliding the tip over the base

is there a situation where this doesn't work?

[full forum]

@wide estuary Has your question been resolved?

[deft zodiac]

i dont think so, it shld always

[neat bay]

so basically acute triangles can do any area ≤ 25/2

and can't do areas > 25/2

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[silent kite]

how do I do this?

[cerulean cargo]

do you know the midpoint formula

@silent kite

[silent kite]

I forgot it

[cerulean cargo]

well it's super simple

I'll tell you

$(\frac{x_2-x_1}{2},\frac{y_2-y_1}{2})$

[glossy valve]

WOWWA

[cerulean cargo]

these represent the midpoint coordinates

[silent kite]

thank you!!

[cerulean cargo]

do you know how to solve from here

[silent kite]

I think I know how to

[cerulean cargo]

I'd let x_2 and y_2 represent point B's coordinates

ok cool

[full forum]

@silent kite Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[boreal hare]

Hi

[boreal hare]

I need help

8th grade math

How do i solve

I dont want solution just the way to solve it

[vast fossil]

Substitute AM = 2MB/3 into AM + MB = 80

[boreal hare]

Thanks

Hm

I got the answer

It says its wrong

Is there anything specific?

Nvm i got it

[full forum]

@boreal hare Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[delicate gust]

Hey can someone explain how trig sub gives this

[delicate gust]

I thought we have to replace x with 4/3 sec theta here

oh i see, how did sec u get in the numerator?

i have 1/(4/3 tan u * 4 sec u)

[topaz valley]

x = 4/3 tan u

dx = ?

[delicate gust]

ohhh i forgot that part

thanks

Where would I go from here ?

what do i sub for t though

[topaz valley]

nah it isnt t sub

at least i dont think

oh no

its

csc

[delicate gust]

wait what

is t sub same as u sub

[topaz valley]

they probably mean the weierstrass substitution

in this case it would work but

the answer is kinda yuck in the end because i think thats the cosecant integral

[delicate gust]

wait isnt integral of csc x just ln|cscx-cotx|+C

or is that diff

[topaz valley]

oh

if you know it then its fine then

if you dont then you would have to do a derivation somehow

t-sub is probably the most direct way

[delicate gust]

i havent learned weierstrass sub in my class so idk if we can use it on the test

[topaz valley]

yeah if you know csc integral

then you're fine

[delicate gust]

Can u check my work please sorry it’s kinda messy

Idk the answer I searched it up and there are multiple versions

wait does inside of the parentheses at the end simplify to 1

that doesnt seem right

[topaz valley]

no it doesnt simplify

,w integral of 1/(x sqrt(9x^2 + 16))

[glossy valve]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 夢雪#2250

[topaz valley]

,w simplify -1/4 arccoth(1/4 sqrt(9x^2 + 16)) - 1/4 ln((sqrt(9x^2 + 16) - 4)/(3x))

[glossy valve]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by 夢雪#2250

[topaz valley]

look like you're missing some stuff

no

wolfie is just being pepega

you're good

except well

your thing is only defined for positive x

you need to keep the absolute value in the log

[delicate gust]

wait wym im good

is it fine?

im confused i havent learned hyperbolic trig 😭

[topaz valley]

yes

you are fine

dw about wolfie

wolfie is just confused

,w simplify -1/4 arccoth(1/4 sqrt(9x^2 + 16)) - 1/4 ln(|(sqrt(9x^2 + 16) - 4)/(3x)|)

still doesnt work

[full forum]

@delicate gust Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[full forum]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[muted kayak]

Hey, im just doing some work I missed but how would you go about doing these?

[proud willow]

should be 1 I think

because since tangent is positive and because it’s between 0 and 180, it can only be in first quadrant

[muted kayak]

I was wondering how youd solvve these type of questions. What's the topic for it callled?

[proud willow]

trigonometric equations?

I think

[muted kayak]

hmm ok

[sharp vine]

it's not 1

[sullen thicket]

AOPS Intermediate Algebra by Richard Rusczyk
If anyone has this book's please send the pdf.

[sharp vine]

if it was tan(theta) = 1 then it would be 1

[proud willow]

oh my bad

ohhh right

so range is from 0 to 720?

[muted kayak]

the mark scheme says 4 yeah

not 1

[sharp vine]

because tan(4 theta) is horizontal compression

so it makes 4 solutions instead of 1

you can solve it manually also, do you know for what 'x' we have tan(x) = 1?

[muted kayak]

wdym?

[sharp vine]

for what angle θ tan(θ) is equal to 1

[muted kayak]

45?

[sharp vine]

yes

[muted kayak]

so would you divide it by 4 since its compressed?

[sharp vine]

close, but

now we add period of tanθ which is 180 deg

hence tan(θ) is 1 for 45, 45 + 180, 45 + 360 etc.

[muted kayak]

ohh then divide by 4?

[sharp vine]

to solve tan(4θ) = 1 it's enough to equate 4θ to 45 + n * 180

and then divide by 4

yes

from here you can check how many solutions lie in the given interval

[muted kayak]

Im still a bit confused on how you would do this if it was cos and 360 instead

[sharp vine]

you mean cos(4θ) = 1 for 0 < θ < 360?

[muted kayak]

yeah

[sharp vine]

then same thing can be applied

cos(θ) = 1 if θ = 0, 360, 720, ...

[muted kayak]

how would you know how many solutions

to go

[sharp vine]

cos(4θ) = 1 if 4θ = 360n
θ = 90n

where n is an integer

so for every 90 degrees we have cos(4θ) = 1