precalculus

[prisma prairie]

woah

that means they did it wrong in the book?

[heady jewel]

piece of shite

its 5/6

in the solutions

[prisma prairie]

why you so mean

yeah so that means they got it wrong ?

[earnest nymph]

....

That's why

[prisma prairie]

thats why what @earnest nymph

[earnest nymph]

That's why I the a^(3/6) term is so weird

[prisma prairie]

oh

so like the book got it mixed up ?

[earnest nymph]

Yeah

[prisma prairie]

kk thanks

i wasted 3 hours

trying to solve this and compare it from the books answers

also @heady jewel is super high ego guy

made fun of me

[earnest nymph]

He's is still fine

[prisma prairie]

yeah i dont dont mind

just like hes weird

[earnest nymph]

Actually to us indices is like high school level so it's weird to heard it from a guy who doing degree

[prisma prairie]

yeah

i know

[earnest nymph]

Btw,what degree you taking anyway?

[prisma prairie]

computer scicne

going into second year

[earnest nymph]

Ah

[prisma prairie]

dude im on summer break right now but practicing math everyday

[earnest nymph]

So have u take discrete math yet?

[prisma prairie]

so i wanna be better at math

[willow bear]

discrete != discreet

[earnest nymph]

Oh sorry sorry

[prisma prairie]

yeah i finished discrete math it was really easy for me compared to calculus

my fav math course is discrete

[earnest nymph]

Nice

[prisma prairie]

i really suck at calculus so i wanna improve my algebra

yeah bro

[earnest nymph]

Well good luck and hope you get better

[prisma prairie]

how long does it take to master pre calcculus?

thanks

[torn swift]

Depends

No set answer to that

[earnest nymph]

Erm... depends on the person

[prisma prairie]

oh

okay

[torn swift]

All depends on aptitude, dedication, and resources you use.

[prisma prairie]

true

[earnest nymph]

But don't pressure yourself if you took a longer time than others to master it

[prisma prairie]

yeah

true

i got all these books from the library that ive been using

idk this work book that im using right now has 2 mistakes so far

it sucks

[earnest nymph]

😂

[prisma prairie]

and i waste time trying to do em

and it never works out lol

so yeah

what grade are you in big good

or college

uni

and amphy too

[torn swift]

Khan academy is great to use as well

[prisma prairie]

just curious

oh oka

thanks

[torn swift]

3rd year Mech E

[prisma prairie]

nice

[earnest nymph]

I finish A level, waiting to enter uni to start my degree

[prisma prairie]

oh nice

good luck everyone

@earnest nymph why did you say not to make the negative exponents positvie btw?

in that question we were trying to do

[earnest nymph]

You gonna have fractions within fractions

It's better to use the indices law (a^m)(a^n) = a^(m+n) and (a^m)/(a^n) = a^(m-n) to solve this

[prisma prairie]

=tex \frac{\sqrt{a}\cdot \frac{1}{a^{\frac{2}{3}}}}{a^{\frac{3}{6}}}

[prisma prairie]

=tex \frac{\frac{\sqrt{a}}{a^{\frac{2}{3}}}}{a^{\frac{3}{6}}}

[prisma prairie]

first pic = second pic right?

by the mathbot thing

just curious

[earnest nymph]

Yes

[prisma prairie]

ok

[clever swallow]

Odd functions multiplying with each other always turns into a even function right?

[earnest nymph]

Yes

[clever swallow]

If I write formal proof on it.
Would It be reasonable to say the exponents are always even therefore the functions are even?

[earnest nymph]

What the actual question?

[willow bear]

@clever swallow no

you should use the definitions of an odd function and an even function

[shrewd urchin]

@willow bear I don't understand this

[earnest nymph]

Mechanics

Fun stuff

[shrewd urchin]

🤔

This is trig for physics chapter

[earnest nymph]

Ah

[shrewd urchin]

I have to know this in order to suck less

[earnest nymph]

I think I can help

[shrewd urchin]

Yea please help

Homie

[earnest nymph]

Since v (given) and g is constant, the only way to change R is to change theta

And R will be max if sin(theta) is max

[shrewd urchin]

I just can't understand why sin sin20<=1

[grizzled orchid]

,w plot sin x

[obsidian monolith]

Display results online and refine query

Requested by hegel#5301

[grizzled orchid]

look at the peak of the sin wave

[earnest nymph]

^

[shrewd urchin]

It's 1 bruh

[earnest nymph]

sin(x) is always between -1 and 1

[grizzled orchid]

[shrewd urchin]

It's the local max

Or wait

It's a global max

[grizzled orchid]

$\sin 2\theta$ is less than or equal to $1$ because that's a property of the sin function lol

[obsidian monolith]

hegel:

[shrewd urchin]

Can a point be global and local max ?

[grizzled orchid]

yes

[earnest nymph]

Yeap

[shrewd urchin]

Ok

[grizzled orchid]

in fact that's a characteristic of all extrema of sin functions

unless you are working over an interval but

w/ever not important

[shrewd urchin]

Yeah I asked because it's local max over some intervals asswell

[primal karma]

it's a hyperbola as well

[willow bear]

not quite

[primal karma]

what is happening to ann

[shrewd urchin]

🤔

I think she is indirectly telling you that you are wrong or partly wrong

[primal karma]

i am referring to her 1/2 1/4 and now 1/8 .__.

[earnest nymph]

Zeno Paradox?

[primal karma]

but where are the other 3/4s of ann , are they gone already and if not where do we store them, we're gonna need to store them for quite some time

[shrewd urchin]

IN the above they say {(x-1)(x+4)}/{x-3} is equivalent to (x-1)(x+4)(x-3)<0

How is this valid ?

[primal karma]

what

how was that rude

[shrewd urchin]

Wot ?

I don't got u ?

I think it's a rypo

@willow bear can you read the solution and tell if it's correct

[willow bear]

the one you posted from your book?

[shrewd urchin]

Yes

[willow bear]

yes it is correct

[shrewd urchin]

How 🤔

[willow bear]

how what

i mean, starting from (x-1)(x-4)/(x-3) < 0, you can multiply both sides by (x-3)^2, a quantity which is positive for all x besides 3

the inequality is not defined for x=3 anyway

[shrewd urchin]

Hmm makes sense thanks you

https://cdn.discordapp.com/attachments/587331244816334849/597072989158244364/2019_07_06_20.04.32_edit.jpg

[viscid thistle]

why did you post this in here

anyone knows...

[opaque shard]

10

[willow bear]

,rotate -90

[willow bear]

ok, what is giving you trouble here @opaque shard

[opaque shard]

Why can't I do this using

-√a²+b² +√a²+b²

[willow bear]

what are a and b

[opaque shard]

Coefficient of sin and cos

[willow bear]

...

what

what are you even talking about

$-\sqrt{a^2 + b^2} + \sqrt{a^2 + b^2}$ is just 0

[obsidian monolith]

Ann:

[opaque shard]

I meant comma instead of plus

[willow bear]

but this is not in the form $a \cos(\theta) + b \sin(\theta)$.

[opaque shard]

How to apply this in case of mod

[obsidian monolith]

Ann:

[willow bear]

so what you sent does not apply.

[opaque shard]

Hmm

So what would be the graph of this expression

[willow bear]

of this FUNCTION.

[opaque shard]

Yes

[willow bear]

i mean if you're interested in the graph

go to desmos and plot it

[opaque shard]

What's that

[willow bear]

http://desmos.com/

[opaque shard]

Ok thanks

If doesnt even have option for absolute value function

[torn swift]

just use | | on your keyboard

[primal karma]

if you ever have a calculator without absolute values just use sqrt(x^2)

[torn swift]

you really need a calc for abs values?

[primal karma]

no, if you have them inside a calulation and are too lazy to think

[shrewd urchin]

Lmao

[primal karma]

thinking is difficult it takes effort

[shrewd urchin]

[viscid thistle]

[hard hornet]

Recall your trig identities

[rough blaze]

shouldn't shifting the point (-4,2) to (0,0) be the same as shifting the point (2,2) to (0,0)?

[limpid moss]

yep, since it's a periodical function with a period of 6

[rough blaze]

I wrote a formula of shifting f(x) from (2,2) to (0,0) and it was marked wrong. What did I do wrong with the formula?

[grizzled orchid]

you may not have simplified

[limpid moss]

it's likely it resulted in something like cos(x+2pi)

where you can just cut the 2pi out

[grizzled orchid]

i see up there you wrote $\frac{\pi}{3} - \frac{2\pi}{3}$ rather than $-\frac{\pi}{3}$

wot

[obsidian monolith]

hegel:

[rough blaze]

The correct answer was in this form

[willow bear]

you forgot the x, for one thing

[limpid moss]

oh yeah lol

[grizzled orchid]

o that oo lol

*too

[viscid thistle]

how would you condense this?

[torn swift]

there is a minus sign I see that we can bring back into the log which will simplify the 1/2

$\log_{a}(b^{n})=n\log_{a}(b)$

[obsidian monolith]

⚡Amphy⚡:

[viscid thistle]

so 1/2 would have the -1 as the exponent?

[torn swift]

yes

[viscid thistle]

okay

[torn swift]

and (1/2)^{-1} is?

[viscid thistle]

2

[torn swift]

good

[viscid thistle]

thanks

[torn swift]

[viscid thistle]

what does it mean by base e?

[limber bone]

e^

[viscid thistle]

so e^7=16?

[frozen needle]

$e^{\ln(16)}=16$

[obsidian monolith]

Tuong:

[native sequoia]

tyson can u send a pic of more of the question?

[viscid thistle]

okay

[torn swift]

you need to use change of base formula

[frozen needle]

that's something kinda important you should know about already

[torn swift]

please do read your eBook then

very powerful resource

[viscid thistle]

i tried using natural log but answer turned out wrong

[earnest nymph]

Can you show your working?

[viscid thistle]

okay

how do i show it?

[earnest nymph]

I don't know? Type it out?

[torn swift]

MS Paint

[wraith idol]

Take a picture

[willow bear]

@viscid thistle do you have your working on a piece of paper or what

[rare galleon]

If you understand the ln and e properties you can isolate t

[stoic quarry]

i have no idea what to do v.v i plugged it into a calculator but all i got was this

[stoic quarry]

hi

[wind igloo]

"To draw the graph plot all points corresponding to x-intercepts, minima and maxima within one cycle"...

[stoic quarry]

okoko tyvm!

i will

[shrewd urchin]

I know that

So the time at which bib is 50% ahead of alice

Is

5t=1.5*3(t+20)

So t=180sexond

Seconds

Assume that the arthimetics is correct

[frozen needle]

$f(2x)=\frac 2{2+\frac 12\times(2x)}$ for all $x>0$

[obsidian monolith]

Tuong:

[shrewd urchin]

You mean 2/2+x

2f(x)=4/2+x

Right

[frozen needle]

I mean what I exactly wrote

[viscid thistle]

lol

[shrewd urchin]

2f(x)=4/2+x

[viscid thistle]

krishna, you're given f(2x), not f(x)

[shrewd urchin]

Ok

I am confused

😭

[viscid thistle]

so if $g(x) = 2x$ then $(f \circ g)(x) = \frac{2}{2 + \frac12 g(x)}$

[shrewd urchin]

Why I am feeling so dumb

Why did you composed f and g

[viscid thistle]

because that's what we were given

[shrewd urchin]

[short sorrel]

we know f(2x), he let 2x = g(x) and thus we know f(g(x))

this isnt really necessary intuition though

we can see

$f(2x) = \frac{2}{2 + x}$

[obsidian monolith]

Namington:

[short sorrel]

and we're trying to figure out what f(x) was

the (2x) meant that, whenever we had an x in the original f(x)

we replaced it with 2x

so let's look for everywhere there's a 2x

$\frac{2}{2 + x}$ can be rewritten as $\frac{2}{2 + \frac{1}{2}\cdot 2x}$

[obsidian monolith]

Namington:

[short sorrel]

so, $f(2x) = \frac{2}{2 + \frac12 \cdot 2x}$

[obsidian monolith]

Namington:

[short sorrel]

as i said above, f(2x) is f(x) with all the x replaced with 2x

so let's go backwards

replacing the 2x with x

$f(x) = \frac{2}{2 + \frac{x}{2}}$

[obsidian monolith]

Namington:

[short sorrel]

we can check our work by plugging in 2x and seeing that we get our original f(2x)

now, find 2f(x)

and we're done.

[rugged ice]

I just need a quick refresher, when finding the coordinates of a negative angle, they are the same as the angle's positive, but flipped to the diagonal quadrant?

[vernal rapids]

They are the same as the positive angle, but the y value if multiplied by -1

You are going down instead of going up

[willow bear]

$N := 10a + b; ; a, b \in { 0, 1, ..., 9} \
P(N) = ab \
S(N) = a + b$

[obsidian monolith]

Ann-iversaire:

[willow bear]

@shrewd urchin this should suffice

i hope you can continue from here

[viscid thistle]

fuck simon and fuck his favorite factoring trick

[shrewd urchin]

You can't disrespect that guy

Is the number 09

$ab+a+b=10a+b \implies -9a+ab=0 \implies a(-9+b)=0 \implies a=0 ,b=9$

[obsidian monolith]

My homies are good at math:

[shrewd urchin]

Or 90

That number is 90

N IS 0

[willow bear]

you meant a = 0 OR b = 9, ok

and a can't be 0 since that'd make the number single-digit

[shrewd urchin]

N IS 9

[willow bear]

no

[viscid thistle]

they asked for the unit digit of N, not N itself

[willow bear]

N can be 19, 29, 39, etc up to 99
but its units digit, which is what you were asked for, is 9

[rugged ice]

I know this is quite easy, but I've been working at it for some time and can't come up with an answer choice that's provided. Someone mind walking me through it?

[shrewd urchin]

@rugged ice draw a diagram

[rugged ice]

I did

[shrewd urchin]

Show

[shrewd urchin]

tan=opposite side /adjacent side

[rugged ice]

I know how to solve it, I'm just not getting an answer that's provided

[shrewd urchin]

,w tan27°

[obsidian monolith]

Display results online and refine query

Requested by My homies are good at math#4971

[shrewd urchin]

tan27°=0.51

,w calc 48*0.51

[obsidian monolith]

Display results online and refine query

Requested by My homies are good at math#4971

[viscid thistle]

lol

[shrewd urchin]

You are not overrated lol

[viscid thistle]

why does it say 191

[shrewd urchin]

They indirectly said f(3,2)=3+f(2,1)

Oh that

[viscid thistle]

hm wait actually

[shrewd urchin]

That's the hint nunber

[viscid thistle]

there

[spring thunder]

oxide the lad

[viscid thistle]

lad

[shrewd urchin]

@rugged ice $24.8\approx24.5$

[obsidian monolith]

My homies are good at math:

[shrewd urchin]

Time murder like this isn't good for my health

[rugged ice]

God I'm too exhausted for this

@shrewd urchin You were wrong, by the way.

[shrewd urchin]

How 🤔 😭

[rugged ice]

¯_(ツ)_/¯

[viscid thistle]

lmao

,w tan(63 degrees) * 48

[obsidian monolith]

Display results online and refine query

Requested by Oxide#5973

[viscid thistle]

@rugged ice

[rugged ice]

im too exhausted to redo the assignment

sitting down and doing online work every day is killing me

[spring thunder]

do online work and stand up then

or just sit down and do nothing

[viscid thistle]

lol

[spring thunder]

[rugged ice]

hilarious

[viscid thistle]

it is

anabolism is occuring in my muscles

[spring thunder]

all these molecules being synthesised to make you move

[shrewd urchin]

Lmao

problem is hard

It's hard it's very hard 😭

@viscid thistle cat how did you become so good at problem solving

[viscid thistle]

i did not

[karmic topaz]

ok nerd

[viscid thistle]

@karmic topaz nerd

[spring thunder]

ok

[shrewd urchin]

Tbh all mathies are nerd

[prisma marten]

[rough hatch]

$\csc^{2}(x) = \frac{1}{\sin^{2}(x)}$ and $\sin^{2}(x) + \cos^2(x) = 1$, so how come $\csc^{2}(x) \neq \frac{\sin^{2}(x) + \cos^{2}(x)}{\sin^{2}(x)}$

[obsidian monolith]

Cirno:

[rough hatch]

am i having a retard moment?

oh yeah i am

thats just 1 + cot^2(x)

many such cases

[shrewd urchin]

@viscid thistle I found answer to rhe yesterdays problem

f(5,2)=19

[shrewd urchin]

The position of particle moving along the x-axis varies with time t according as $x=a\sin(\omega*t+\theta_0)$
Where $a,$ $\omega$ and $\theta_0$ are constant.($\omega$ is non zero )
Let $x_1$ and $x_2$ be the position of the particle at different time instants $t_1$ and $t_2$ respectively. Find $t_1-t_2$ if\
a)$x_1=x_2$ \
b)$x_1-x_2=2a$ \
The answer of a) and b) are $\frac{2k\pi}{\omega}$, k is an integer) and $\frac{(2t-1)\pi}{\omega}$ , t is an integer

[obsidian monolith]

My homies are good at math:

[shrewd urchin]

You can only use unit circle to answer this question

[viscid thistle]

@shrewd urchin

f(5,2) = 19
i know, i solved it in front of you

[shrewd urchin]

I solved this on my own

f(1,0)=5

f(2,2)=2+f(1,0)

[viscid thistle]

amazing

[shrewd urchin]

f(3,1)=3+f(2,2)

f(4,3)=4+f(3,1)

f(5,2)=5+f(4,3)

[spice cloud]

Wassap

So my teacher just asked us to construct a graph for x^4-36y^2=0 and wolframalpha just pooped out a 3d graph

Halp

[pale kettle]

probably because you left out the = 0 part

[heady jewel]

lmao rip onion

[spice cloud]

Lol yeh

Just found out

How do I get the solution though

[heady jewel]

youre in class?

[spice cloud]

No sirry

Im at home

[spring thunder]

yea rip onion

[shrewd urchin]

,w range of f(x)=3\sqrt{2x-7} -8

[obsidian monolith]

Display results online and refine query

Requested by My homies are good at math#4971

[shrewd urchin]

,w domain of f(x)=3\sqrt{2x-7} -8

[obsidian monolith]

Display results online and refine query

Requested by My homies are good at math#4971

[shrewd otter]

Could anyone help me solve for x?

[frozen needle]

what's giving you trouble here ?

[shrewd otter]

im not very good with logs so im just getting confused

[royal gull]

do you know properties of logarythms?

Like, what happens when you add or subtract them when they have the same base?

[shrewd otter]

ooh

do you multiply them?

[royal gull]

no

I mean

when you add, then yes, you multiply the arguments

[shrewd otter]

ye sorry thats what i meant

[royal gull]

but you are dealing with a subtraction here

[shrewd otter]

but how would i get rid of what's in the parenthesis

id put in in a fraction first

[royal gull]

$\log_a x + \log_a y = \log_a xy$

[obsidian monolith]

dog:

[royal gull]

$\log_a x - \log_a y = \log_a \frac{x}{y}$

[obsidian monolith]

dog:

[royal gull]

try to use this

[shrewd urchin]

Need help with d)

I think d is commutative

Is it?

[vernal anchor]

well, why do you think that

[shrewd urchin]

Coz they have told that ♧ and ♡ is commutative and if they are commutative then ◇ has to be commutative @vernal anchor

y◇x=(y♧x)♡{x♧y} which is totally equivalent to x◇y

[vernal anchor]

exactly

[next willow]

What if only heart was commutative?

It was a question to krishna ugh..

That's a pity

[vernal anchor]

damn

i can still redact

[next willow]

How a beautiful day

[vernal anchor]

im wondering why this question has a star next to it

[spring thunder]

cause it's * hard *

[vernal anchor]

in (a) star is a binary operation though

but ok

im currently taking some CS class and the prof is rating hw with chilis

[spring thunder]

(d) star Suppose...... = ?

[vernal anchor]

from 0-3 chilis

[next willow]

Mmh that's enigmatic

[vernal anchor]

(d) seems just as hard as the other questions though

[spring thunder]

rate the problems with mniip's heads

[vernal anchor]

it's just mind tricks on the students

it confused Krishna so much, he had to ask for confirmation

[spring thunder]

well that's AoPS if i'm not mistaken

[shrewd urchin]

Yea

It is

[vernal anchor]

does the star mean it's hard?

[shrewd urchin]

Yes @vernal anchor

But it wasn't hard at all

I was just confused why they gave * for such an easy problem

[eternal crown]

I have an exercise and it's simply
x^2 -4xy +8y^2 +4x -4y +6 = 0
what kind of conic is this?

[wicked swan]

@eternal crown wait i might take back what i said. im not sure whats going on with the -4xy term

[eternal crown]

yeeeees that's what's giving me trouble, I only know the kinda "simply" way

I saw some matrix were involved but I have no clue of how to use t hem

that's why I asked in linear algebra

[wicked swan]

do you have a screenshot or picture of this question?

[eternal crown]

it's in portuguese but it's what I said

the conics and degenerations are the alternatives

[wicked swan]

according to desmos it would be a unique point. hmm its not that obvious to me tho. You said the solution used matrices?

[eternal crown]

yes

yeah that was deleted

[wicked swan]

weird no idea how they came up with that. I think you could ask #linear-algebra if you want. You should probably add the given answer for context tho.

[eternal crown]

if only I had it

[wicked swan]

had what?

[eternal crown]

the answer

[wicked swan]

this is how they present it tho: https://cdn.discordapp.com/attachments/363224154469826562/598371510935224320/21857f15e486a1fc900c583afe2689b5e729a60d.png
post that

[rugged ice]

I don't understand how I'm supposed to get a second answer here, can someone explain?

[torn swift]

Well let’s look at the unit circle

tan(x) is positive where and where?

[rugged ice]

In the first and second quadrants

[prisma marten]

check again

[rugged ice]

Positive in what regard?

[torn swift]

Where the output of tan(x) is positive

There are two quadrants where that will happen

[rugged ice]

It's positive in the first and second quadrants on my graphing calculator

[torn swift]

What signs do cosine and sine have in quadrant 2?

[rugged ice]

I don’t know

[torn swift]

You know of the unit circle though? That is why I ask you to refer to that.

[rugged ice]

A bit I guess, but I still don't understand what I'm supposed to do.

[torn swift]

Do you know how x and y are related to cosine and sine on the unit circle?

[rugged ice]

Yes

Cosine being represented by X and Sin with Y, yes?

[torn swift]

Yes

And now consider quadrant 2

What sign will x values have?

What sign will y values have?

[rugged ice]

X will be negative, Y will be positive

[torn swift]

Then tan will be positive or negative?

[rugged ice]

Negative?

[torn swift]

Remember that tan(x)=sin(x)/cos(x)

So the tan(x) will be negative in quadrant 2

So let’s look for when both x and y are negative, that will give a positive value for tangent

[rugged ice]

So quadrant 3

[torn swift]

Yes

So tan(x) is positive in which two quadrants?

[rugged ice]

1 and 3

[torn swift]

Correct, very good

To get from an angle in quadrant 1 to quadrant 3 you add how many radians?

[patent beacon]

I like to think of tanθ as the slope of the line between the origin and (x,y)

That is all

[rugged ice]

pi/2?

[torn swift]

not pi/2

[rugged ice]

or 2pi

[torn swift]

it will take more than pi/2

well try this

draw an angle in quadrant 1

and now extend the ray so that it is in quadrant three

[rugged ice]

I don't have graphing paper on me right now

[torn swift]

we can use wolfram to illustrate this then

let's take a 45 degree angle then

,w graph y=x from 0 to 1

[obsidian monolith]

Display results online and refine query

Requested by ⚡Amphy⚡#0697

[torn swift]

that forms a 45 degree angle

and now to form that same angle in quadrant, I just mirror this line about the origin

,w graph y=x from -1 to 1

[obsidian monolith]

Display results online and refine query

Requested by ⚡Amphy⚡#0697

[torn swift]

so that is a 45 degree angle in quadrant 1 and quadrant 3

and how far apart are the angles from each other?

this line forms a ? angle

[rugged ice]

180 degrees

[torn swift]

which is how many radians?

[rugged ice]

pi

[torn swift]

very good

so you solve tan(x)=2.75 for x in radians I am assuming, and then to get a second answer you will do what?

[rugged ice]

Add pi

[torn swift]

yes, and can you tell me why you do that?

[rugged ice]

To find the value on the other end? I don't know.

[torn swift]

Can you explain to me again why there are two values for tan(x)=2.75 in the first place, and how to find the second value once you solve for the first value, which will be in quadrant 1 when you use a calculator to solve it

[rugged ice]

There are two values because of the unit circle, we find the second by adding pi, finding its other positive equivalent

[torn swift]

can you be more specific about the unit circle part

[rugged ice]

I don't think I can

[torn swift]

I mean we talked about just 10 or so minutes ago

you should review our convo to see why it was quadrant 1 and 3

[rugged ice]

It's on the equivalent place on the opposite half of the circle?

[torn swift]

I was looking for you to explain why tangent is positive in those two quadrants

[rugged ice]

Because both X and Y are positive in quadrant one, and they're both negative in quadrant three; resulting in positive answers

[torn swift]

very good

don't forget to say that on the unit circle, cos(x) is represented as the x coordinate, and sin(x) is the y coordinate

[quick dagger]

i think this is a precalc q but how would i solve sin x = 1/2

i know the answer is 60 degrees bc i guess and checked but can someone teach me the official way

[limpid moss]

it depends on what you'd call the 'official way'

[quick dagger]

wait is it 60 degrees?

[limpid moss]

and yeah it's 30

[quick dagger]

can you teach me how to solve it

[limpid moss]

if you're not using calculus or anything like that to solve it, you'd use trigonometry

[quick dagger]

how so

[limpid moss]

you'd draw a right triangle and make it such that according to the definition of a sine

the length of the hypotenuse and the non-adjacent side to the angle would have a ratio of 2:1

[quick dagger]

how so?

oh is it bc sin is op/hyp

so opp = 1 and hyp = 2?

[long pond]

http://mathcentral.uregina.ca/QQ/database/QQ.09.05/gary1.1.gif

[limpid moss]

yeah pretty much like that

[quick dagger]

what does the left side say?

[long pond]

sqrt(3)

sorry bad imag

[limpid moss]

anyways that's a special triangle, and you can duplicate the triangle and flip it over

that would make an equilateral, and since the angle we're looking for is the half of an angle of an equilateral, the angle is 30 degrees

you can use this geometric method only for special cases where the angle would be 30, 45, or 60

which is why you only memorise the sine for the three angles

[quick dagger]

is it 30 degrees bc the opposites of the shorter sides of the triangle is the smaller degrees?

[spark cliff]

how do I do this word problem 😦

[quick dagger]

wouldnt that be a 45 45 90 triangle

@limpid moss ^^

[limpid moss]

sorry, i don't know what you mean by tha

[spark cliff]

it is

[quick dagger]

@spark cliff so that should be enough evidence to solve it wouldnt it

[spark cliff]

um idk

200 feet!!

is it actually 200 feet wait

cause that’s what I actually got

[quick dagger]

hm

idt thats a precalc q tho

i think its geometry

i did that last year i forgot lol

[long pond]

yes, it is a 45-45-90 triangle, so the legs are equal in magnitude

@quick dagger one thing to note is that that equation has more than one solution

[quick dagger]

what eq?

@long pond idk how to do this

[long pond]

sin(x) = 60

er

mb

sin(x)=1/2

this equation has more than one solution

[limpid moss]

yeah but that's only for people who think adding 2pi is a solution that isn't nominal

[quick dagger]

like would sin x = 1/1.33 be 60 ?

@limpid moss

[limpid moss]

no, within the scope of a triangle's angles, or 0 to 180 degrees

[spark cliff]

this does make sense 🤠

[limpid moss]

there's only one solution for all trig functions

[quick dagger]

@limpid moss so its not 60? for sin x = 1.33

[limpid moss]

if you meant sin x = 1/1.33, then yeah there would be a different answer for that

[long pond]

you might think of it in words: what is the angle such that if you take it's sine, you obtain 1/2 @quick dagger

if you memorized your trig values, this should be easy

[limpid moss]

there's only like 3 of them anyways

[long pond]

there's infinite

[quick dagger]

i havent taken precalc or anything

im going to physics so i need to know

[limpid moss]

who memorises angles other than 30 45 and 60

[quick dagger]

what trig values?

[long pond]

yeah

[limpid moss]

mostly until you start using calculators for trig functions

trigonometry will mostly be just another way to force you to do calculations you don't want to do

[long pond]

like sin(60) = sqrt(3)/2

cos(60) = 1/2

oh look

a solution to your equation

[quick dagger]

?

[long pond]

cos(60) = 1/2

[quick dagger]

ok

[long pond]

er

[limpid moss]

do you know the identity sin^2 + cos^2 = 1

[long pond]

sin(30) = 1/2

[quick dagger]

i said i havent taken precalc

only alg 2 and below

[long pond]

i learned this in alg 2

[quick dagger]

i didnt

[long pond]

oh

[limpid moss]

yeah i don't know what precalc

[quick dagger]

only graphing sine and cosine

[spark cliff]

same^

[long pond]

if i asked you what tan(45) is could you tell me?

[quick dagger]

no

[limpid moss]

oh dam

it's just convenient if you memorise them

[quick dagger]

why would u expect me to know i said i dont know nothing about this

its just in my ap physics packet for some reaosin

and i havent learned it yet

[long pond]

uh

yeah you will need more of an introduction to trig before you tackle problems like sin(x) = 1/2

try using khan academy or another website on your own time

[quick dagger]

@long pond any video titles i should llook at ?

cause im not sure where to start

[long pond]

uhm hold on

let me find something

[quick dagger]

kk

[long pond]

sorry computer is s l o w

https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles

tbh i'd start here

if you only have experience drawing sin and cosine waves

just click the first article

you can skip over smething if you already know it

[quick dagger]

@long pond and this will teach me how to solve sin x = 1/1.33?

[long pond]

well, eventually

[quick dagger]

oh

cause this packet is due in a month

and like 3 weeks

like aug 22

[long pond]

if you can't tell me what basic trig values are, you will have to def. learn that

this is a streamlined and organised method

[quick dagger]

@long pond what is sin x = 1/1.33 question name ?

like what category does that q fall under

[long pond]

hold on, I may have to give you something else as well

https://www.khanacademy.org/math/trigonometry/trig-equations-and-identities

this goes into how to solve trig equations

[native sequoia]

the category is using arcsin on calculator

[long pond]

but before you do this, you should be familiar with the basic trig function and what you can do with them

[quick dagger]

when i go into ap physics, would i have to learn trig?

@long pond bc if i am then ill spend a lot of time learning it now

if i dont have to learn then ill prob just not fully learn it

[long pond]

I can't imagine you wouldn't need to know trig in an upper level physics class

maybe not super in depth, but probably more than you know nw

now*

[quick dagger]

why would the teacher give us this q when we havent even taken precalc

i mean it is ap physics but like we didnt get a textbook

[long pond]

idk

[quick dagger]

@long pond she did give us a warning on the front page saying to watch videos and reearch unknown concepts

and that ill be tested on it when i go back to school

so i might as well learn trig then

[long pond]

yeah i would do that

[zealous sail]

Should I remember all these circles? or should I be able to get these answers on my own

my trig knowledge is very minimal

this is a pre-calc class

What is expected of the student here?

[patent beacon]

@zealous sail
Memorize sin, cos, and tan of the special angles

For example, sin(5π/6) = 1/2, using that diagram

[quasi niche]

The second part of the piece wise isn’t even right?

Because it’s negative if u replace x with a negative?

[patent beacon]

@quasi niche
The first part isn't either

f(x) is not even

[blazing solar]

Any idea how to solve this?

[pale kettle]

What have you tried?

@blazing solar

[blazing solar]

Nothing

I don't know where to start

[pale kettle]

Well then keep thinking

[blazing solar]

ok

[serene heath]

[rare galleon]

If a person is thinking for more than 30 minutes and he doesn’t have a solution yet help him.

[pale kettle]

@rare galleon hey I've been stuck on this research problem for two weeks, can you help me

[prisma marten]

been working on a solution to RH, any help?

[rare galleon]

@pale kettle way different mate, but good try.

[pale kettle]

what's the difference?

Honestly

It's not like he reached out for more help

[blazing solar]

I think i got it

646

[viscid thistle]

@pale kettle are you actually doing reu

[shrewd urchin]

I am doing

[viscid thistle]

you're not even an undergraduate

reu stands for research experience for undergraduates

now cease your trolling

[shrewd urchin]

Actually I am an ug

I am doing research on behaviour of cats

[lyric burrow]

oi boys

[tawny nacelle]

oi

mate

was goin an

[shrewd urchin]

Don't tyep lik dis

[tawny nacelle]

oi not man ??

[shrewd urchin]

Soap you doing physik

[tawny nacelle]

yea

[lyric burrow]

oi mate

need to ask a question

[tawny nacelle]

[lyric burrow]

does one need to purchase a graphing cal?

for precal?

[shrewd urchin]

People who ask to ask must be banned

[tawny nacelle]

no ?

[lyric burrow]

ah ok

I donno where i got the idea from

but ty

[tawny nacelle]

was that it ??

[lyric burrow]

no

mate

[tawny nacelle]

ok lets get to the real question then

[shrewd urchin]

Soap is physik hard ? For u

[tawny nacelle]

yea man

[shrewd urchin]

Ok let me imagine how hard it would be for me

[lyric burrow]

good resources to learn precal in under a month

willing to put in the work

[tawny nacelle]

#resources

also khanacademy is very nice

[lyric burrow]

brother

[tawny nacelle]

https://www.khanacademy.org/

[lyric burrow]

yeh

[shrewd urchin]

Soap is it really hard or u joking

[tawny nacelle]

i learnt precalc from khan academy and look at me i can multiply two number like it nothing

😤

[lyric burrow]

😔

[earnest nymph]

Professor Leonard is always a good choice

[quasi forum]

Hi

Can i have help with part (ii) please?

also i think this should be pre calc(?)

[shrewd urchin]

Yup

roots are rational if Dicriminant is a perfect square

[quasi forum]

yep

but how does that explain if L is rational, therefore roots are rational?

is it since if L isn't rational, you can't form a perfect square?

[shrewd urchin]

let me think

Yeah

If L is not rational then the roots are not rational true

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

[obsidian monolith]

Krishna:

[shrewd urchin]

If b is not rational then how will the roots be rational @quasi forum

I think the quadratic formula itself answers your question

[quasi forum]

oh ok

I was thinking of that as well

but wasn't too sure

[spring thunder]

well it's not hard to show L rational => rational roots

[shrewd urchin]

$x=\frac{-b}{2a} \pm \frac{\sqrt{b^2-4ac}}{2a}$

[obsidian monolith]

Krishna:

[spring thunder]

the discriminant would just be $$L^2-4M = L^2-\frac 89 L^2 = \left(\frac 13 L\right)^2$$

[obsidian monolith]

emeric75:

[spring thunder]

(using part one for the first equality)

ie discriminant is rational

so indeed roots are rational

[quasi forum]

so by proving L is rational, therefore roots are rational?

but isn't the question worded slightly differently?

[spring thunder]

i'm not sure if they want the equivalence or just the way i did

[quasi forum]

Like i get your reasoning

[shrewd urchin]

In which grade are you in

[quasi forum]

but isn't the question asking for all values of L when rational

yr 11 AUS

[shrewd urchin]

What

Yr11 aus

?

You mean 11 grade ? In aus

[quasi forum]

yea

[shrewd urchin]

Lol

$ x^2+\sqrt{7}x+1=0$

[obsidian monolith]

Krishna:

[shrewd urchin]

D is rational but roots aren't

Or that rules works only if a,b,c are rational number

[quasi forum]

D?

[shrewd urchin]

Discriminant

[spring thunder]

well we also know that L is rational in the q

[quasi forum]

oh wait

since we know L is rational

we can use discriminant

hence, roots are rational

^plus everything else i skipped on 😃

[shrewd urchin]

Yup

How did you proved 2L^2=9M

[quasi forum]

find one root

then sub it in

Wait why?

[shrewd urchin]

$x=\frac{-L\pm\sqrt{L^2-4M}}{2}$

[obsidian monolith]

Krishna:

[quasi forum]

hm?

[pale kettle]

@viscid thistle I am actually doing reu?

[heady jewel]

@quasi forum did you learn vietas formulas yet?

[heady jewel]

that problem would be bollocks if you knew it

,w vieta formula

[obsidian monolith]

Display results online and refine query

Requested by Lionel#5497

[sterile portal]

im kinda confused on how to answer this

[torn swift]

Can you say anything about the two right triangles?

[sterile portal]

they're similar triangles

[torn swift]

So you can use proportions to set up an expression that includes x then solve for x

[sterile portal]

would it just be x=(rt/h)-t?

[torn swift]

I didn’t work it out, no idea lol

[sterile portal]

oh but u start with r/x+t=h+t and then just solve for x

[torn swift]

Seems like it should be that

h/t you meant?

[sterile portal]

yea lol

[torn swift]

Ok you have the correct starting proportion

[sterile portal]

like one triangle equals the other cause theyre similar

[torn swift]

Will assume you did the algebra correct

[sterile portal]

ok thanks

[torn swift]

Then x is equal to what you got

[sterile portal]

yep

[heady jewel]

this is surely precalculus

[sterile portal]

how do I mathematically find the left most point?

[serene heath]

the point with the smaller x coordinate

[wind igloo]

The leftmost intersection will be the one with less positive x coordinate.

[sterile portal]

but how do I find that number?

I have the equation of the line and circle, i just don't know how to find the smallest x-coordinate without guess and check

[royal gull]

input the line in the circles equation

like for y=ax+b

[sterile portal]

OH LMAO i was making them equal each other facepalm

i really went brain dead after exams

[shrewd urchin]

Guys

I got a real quick question

Mm

Can I skip ellipse and hyberbola and goto limits

It's for physics

[heady jewel]

thats what i did

just to learn calculus

[shrewd urchin]

Ok

[heady jewel]

conic help you at a better understanding and pure understanding of calc tho

i mean if you want to do it for the sake of problem solving

skip conics

[shrewd urchin]

I want to understand only for physics

I am doing first course on physics

It's a basic one but needs a little bit of calculus

If I need ellipse and hyper bola I will learn it later

[heady jewel]

like kinematics and other shi?

[shrewd urchin]

Yes

[heady jewel]

like newtons laws

[shrewd urchin]

Yup

[heady jewel]

ok then just study basic calc

its all you need

standard integration,derivatives and easy limits

[shrewd urchin]

Khan acamdey has a basic course in that

Like math for physics

Also I want to know basics of calculus

Because I will do some math after 2 months that need a little calculus .

[heady jewel]

while you learn the true meaning of derivative

you will have a lot of fun

its satisfaction know how shit goes on in very small places

[shrewd urchin]

Differential coefficient

[heady jewel]

whats that

[shrewd urchin]

That's dedicate

Derivative *

[heady jewel]

oh ok

[serene heath]

I never bothered to learn comic sections

[shrewd urchin]

Hmm

[serene heath]

[shrewd urchin]

Even I am skipping it

[shrewd urchin]

Boi @heady jewel ? Are you there ?

https://www.khanacademy.org/science/in-in-class11th-physics/in-in-11th-physics-differentiation
Here is the course of basic calculus can you tell if this is enough for physics

This is the link .

[silk sequoia]

how do you do this one?? i feel like theres something about angles here i dont know about that im missing

[torn swift]

I have my vote on what the answer is

think carefully about those restrictions on the angles and the two relations you have

[silk sequoia]

ohhh wait

its like that thing where sin60 and sin 120 are equal

but cos60 and cos120 are not because one is negative

so it has to be C

right?

[torn swift]

thinking it's that as well

[fringe stream]

since theta is between 0 and pi/2, its sine and cosine are gonna be positive

so you can safely say phi is in the second quadrant

but how are you sure its pi - theta and not pi/2 + theta? theyre both in the second quadrant

[torn swift]

frick, I was stuck between the two as well

[fringe stream]

remember, one of those returns the same trig function

[silk sequoia]

??? but if you add 90 degrees to 60 degrees thats not 120

[torn swift]

He’s more or less asking you to justify which one it is

The above is one such justification, albeit numerical, though still valid.

Well it’s partly a justification, to complete the reasoning you have to show that sin(φ)=sin(θ) and
cos(φ)=-cos(θ) is correct when φ=π-θ, and incorrect if you choose π/2 + θ

[silk sequoia]

hmmm

should i use a unit circle to prove?

[torn swift]

That’s fine

[silk sequoia]

ok im not exactly sure what im doing but ill give it a shot

since the first restriction says theta must be between 0 and 90 degrees, sin and cos both must be positive

but the second restriction says Φ is between 0 and 180 degrees, so while sin is positive, cos must be either positive or negative

looking at the top half of the unit circle, the coordinates are nearly the same on both sides if you look at similar angles like 30 vs 150

[fringe stream]

second restriction says phi is between 0 and 2pi

not pi

[silk sequoia]

ohhhh fuck

whoops

but they still need to be similar angles like 30 and 150 for the condition to be true

idk whats the real term for it

you cant get that "matching" degree by adding 90

is that how to explain it or am i missing something

[little lagoon]

ool

[shrewd otter]

"Use the fundamental identities to write the first
expression in terms of the second." What do I do with the Quadrant VI part?

Quadrant IV* woops

[viscid thistle]

use the fact that sin and tan are negative for angles from that quadrant

and cos isn't

[shrewd otter]

sorry im still kinda confused on what to do with that information. Tan t would turn into sin t/cos t, and cos t would turn into the square root of 1=sin^2 right?

so it being in quadrant IV just means its positive?

[patent beacon]

cos(t) = √[1 - sin²(t)]
If in Q4

[limber bone]

how does that include tan

wtf is this problem

[autumn marsh]

woo woo im teaching myself precalc this summer for the upcoming class

I have a question about constrictions of the unit circle. Is it just memorizing or is there logic behind why arctan, arccos, arcsin are constricted to lilke
tan quadrants I and IV
cosine I and II etc

idk if im asking this correctly either

[royal gull]

wut

if ure talkinga bout the sign or value then its clear from the graphs of the function

,w plot cosx

[obsidian monolith]

Display results online and refine query

Requested by dog#3227

[river kindle]

@autumn marsh there is logic to it. You can actually construct it by hand if you wanted to

[autumn marsh]

ill send a pic of my notes

and thats what i thought

I was trying to connect it with ASTC but it didnt make sense to me

[river kindle]

However this is math. Most of everything can be done via logic but memorization is faster

[autumn marsh]

the highlighted stuff

yeah very true XD

i feel like its simple and im overthinking it cuz i tend to do that and make it harder than it rlly is

[river kindle]

Study trig

[autumn marsh]

this is the very beginning of the stuff in the precalc thing im doing, do you think once i practice problems and go further into it ill understand better?

I was pretty solid with trig in alg II

[river kindle]

You dont have a good grasp of trig from what I seen already

[willow bear]

quadrant 6

[rigid beacon]

Mainly the restrictions are because of when you graph the inverse it has to fit the vertical line test

[autumn marsh]

^ that actually registers in the brain

[rigid beacon]

There ya go then

[autumn marsh]

we didnt learn everything in trig @river kindle plus my teacher sucked so i went through hell tryna understand. We missed a lot of stuff for alg II in general but i got high 90s on all the tests for it

a lot of the stuff in precalc regarding trig is a lil different than what im used to seeing

[rigid beacon]

Khan Academy is the best self teaching source until you get to calculus imo

[autumn marsh]

thats what i be usin to take notes and what i used to fill in gaps by my teacher

[rigid beacon]

Use Khan to fill in the gaps

[autumn marsh]

he somehow is allowed to teach precalc honors and im glad im not taking it

hes horrible

[rigid beacon]

Damn

That sucks

[autumn marsh]

i have 5 missing test grades and i asked him to put them in and he said no

literally said nah

[rigid beacon]

We had a bio teacher so bad he got banned from teaching honors and AP

[autumn marsh]

DAMN

banned

[rigid beacon]

And we had a physics teacher so bad he got banned from AP Physics

Yea he's allowed to teach, just only regular level classes

[autumn marsh]

thats icky

my alg teacher made people cry too, he aint the best but idk i feel bad for him too sometimes

we had a sub for like a month and she taught the class for 15 years before he had

loved her, very enthusiastic and loved what she was teaching, also rlly strict and on topic

my style of teacher precisely

[river kindle]

@autumn marsh my algebra teacher threw a desk across the room into a wall once. In either case, my comment was judt me saying get a trig textbook or cheaper or free alternative to brush up on it

Algrebra only scratches the surface

That is what i am doing at least for college precalc

[autumn marsh]

mmk i was just saying im good at alg II trig XD and ill look for some textbooks

[thick star]

can someone help me wif this problem?

i dont get it 😦

[patent beacon]

Gotta bring that exponent down first; know how to go about that?

[thick star]

how do i do that?

[patent beacon]

Log both sides