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#help-10
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
turbid wing
(sin x)^(3/2) + (cos x)^(3/2)
obtuse pebbleBOT
(sin x)^(3/2) + (cos x)^(3/2)
turbid wing
(sin x)^(3/2) + (cos x)^(3/2)
how do I find the range of this
slim cove
are you allowing complex numbers?
turbid wing
the function will repeat after a fixed interval
slim cove
Yes but like for the domain, it's not all real numbers right
slim cove
So only when x is in the first quadrant
turbid wing
yeah
slim cove
Hm that's really tricky, what have you tried so far
turbid wing
I have tried some basic manipulations but didn't make any progress
wait I'll install discord on my phone and send you the pic
slim cove
kk
turbid wing
@slim cove
don't mind the handwriting
I tried using a^3 + b^3 too but it got more complex
slim cove
I was thinking that too, to try to get sin^2 and cos^2 from it but I'm not sure it works
hmm
I'm not sure what to do but it might help if you let u = sin^2 x, then the equation becomes y = u^3/4 + (1-u)^3/4 which looks a little easier to deal with
do you know calculus?
turbid wing
yes
slim cove
I would try taking the derivative of that and finding max/mins ^
turbid wing
you wanna go by differentiation?
turbid wing
I would try taking the derivative of that and finding max/mins ^
yeah
slim cove
Yea
obtuse pebbleBOT
@turbid wing Has your question been resolved?
obtuse pebbleBOT
@turbid wing Has your question been resolved?
turbid wing
<@&286206848099549185>
brave bramble
I think AM-GM can work too
turbid wing
how will they cancel out each other?
@brave bramble
I have got the maxima by derivative. I just need to find the minima now
I tried calculating f''(x) for minima but its getting complex
turbid wing
can't do that in exam
slim cove
I have got the maxima by derivative. I just need to find the minima now
Wait the minima and maxima are found using the same process of setting the derivative to zero
Did you check the boundary points?
turbid wing
yes
slim cove
You don't need the second derivative
turbid wing
then?
slim cove
so there's only one point where the derivative is zero right
turbid wing
I got the maxima. It is 2^1/4
slim cove
yup
turbid wing
yes
slim cove
so the minima has to occur at the boundaries
aka when x = 0 or x = pi/2
etc
so the minimum is 1
which.. just graphed it on desmos and it checks out
turbid wing
can you please tell that how would I know that the minima will be when x=0 or pi/2
?
turbid wing
ah yes and we can't have negative values as the function is inside root
slim cove
yep!
slim cove
no problem!
if you find a way to do it without calculus let me know.. but I have no idea how you would do it without calculus
turbid wing
The guy above said that you can find using AM-GM
but I guess we would only get the minima using AM-GM
turbid wing
.close
split marsh
obtuse pebbleBOT
forest sinew
whats the relationship between these two margins
obtuse pebbleBOT
@split marsh Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
quiet ingot
i am stuck on this math problem. i don’t understand it at all
obtuse pebbleBOT
i am stuck on this math problem. i don’t understand it at all
quiet ingot
tardy epoch
i am stuck on this math problem. i don’t understand it at all
Start by plotting
quiet ingot
like this?
tardy epoch
That doesn't look like a graph
quiet ingot
oh shoot my bad. how do i get to the graph to plot the points
quiet ingot
yes
cyan pagoda
yeah i believe its the rightmost button on the first row
should be maybe graph or something?>
idk
quiet ingot
it pulled up a graph and it’s just blank. i tried pressing multiple buttons but nothing is happening to the graph
this is my calculator
what do i do
cyan pagoda
click graph
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fossil rampart
obtuse pebbleBOT
fossil rampart
Can I get some insight on this?
I know it diverges via the integral test and I know it isn't the nth term test
so A has to be the answer, as it doesn't converge
I feel like that wouldn't be a good comparison given there is some terms where 1/2n is bigger than the function and some smaller
royal basin
are there now
are you sure this isn't a case of "the inequality fails at finitely many points but no more"
slim cove
the only thing that matters is that 1/2n is smaller in the long term
you can show this by taking the difference between 1/2n and (8/n - 8/n^2)
do you know how to calculate $$\frac1{2n} - \left(\frac8n - \frac8{n^2}\right)$$
warm shaleBOT
Eric Tao
fossil rampart
do you know how to calculate $$\frac1{2n} - \left(\frac8n - \frac8{n^2}\right)$$
I do not
so because 1/2n is smaller than the function given it can be compared or?
slim cove
okay so the first step is to put things in a common denominator
royal basin
there is in fact precisely one point where your inequality fails.
slim cove
so because 1/2n is smaller than the function given it can be compared or?
Yes 1/2n is smaller in the long run
obsidian isle
how do you get desmos to do dots
slim cove
which is the only thing that matters for convergence/divergence
fossil rampart
you don't know fraction arithmetic?
my G you would be surprised how little math knowledge I have
royal basin
how do you get desmos to do dots
L = [1...100] then plot (L, f(L)) and (L, g(L)) where f and g are the functions describing the terms of both series and have been defined in previous lines
slim cove
it's literally just what she said lol
royal basin
obsidian isle
oh i see. that's really useful
fossil rampart
There is a good reason I plan on going through a proof based basic math book after this course
royal basin
i mean like, you do still need to know your way around algebra
fossil rampart
took me like 40 hours to do the cylindrical shell homework being dumb
fossil rampart
but do you know how to put the fractions into a common denominator
yeah
slim cove
**Eric Tao**
okay so you can go ahead and do that for this
your task is to show that for n > 1, this is negative
and therefore 1/2n < 8/n - 8/n^2
which means the comparison test can be used
royal basin
yeah
then why mislead us by saying you don't know fraction arithmetic when you clearly do know a nonzero amount thereof :p
fossil rampart
1/2n - 8n-8/n^2 = n/2n^2 - 2(8n-8)/2n^2
slim cove
yep!
royal basin
missing parentheses
slim cove
then why mislead us by saying you don't know fraction arithmetic when you clearl...
the word "thereof" is so funny lol it's been a while since I've heard someone use that correctly
fossil rampart
then why mislead us by saying you don't know fraction arithmetic when you clearl...
I am barely competent in all matters of algebra and basic math, it's a real mixed bag
srsly no clue how i have over a 90 in cal 2 rn
slim cove
tbh if you're struggling on things like that, khanacademy helps
you can just grind away practice on random skills
I spent a lot of time doing that as a kid so I could get the leaf points on my account xD
fossil rampart
I didn't go to highschool so that is where I learned my piecemeal algebra skills to test into cal 1
slim cove
khan academy is all of our heroes
fossil rampart
90% of the entry test was just weird trig questions
slim cove
ahh trig questions they're so annoying
fossil rampart
anyways I think I got why it's an acceptable test, much appreciated math homies
.close
vague mural
hey im curious on what i did wrong in my equation why do i get a different result
obtuse pebbleBOT
hey im curious on what i did wrong in my equation why do i get a different resul...
vague mural
ik i didnt follow the same formula they did but i thought i did everything legally with the rules of math
also sorry for the neck tilt
warm shaleBOT
vague mural
almost
slim cove
ayyy
vague mural
ayyeee
vague mural
L
slim cove
kk
slim cove
so the problem is that when you multiplied $m$ on both sides to $$L = \frac{125}m + 50n$$
vague mural
and correct answer is the one that showed up
warm shaleBOT
Eric Tao
vague mural
when i got it wrong
slim cove
you should have $$m(L) = m\left(\frac{125}m + 50n\right)$$
warm shaleBOT
Eric Tao
slim cove
and then you need to distribute the m to both terms properly on the right
so it should be $$Lm = 125 + 50mn$$
warm shaleBOT
Eric Tao
vague mural
u have to do that?
wait u have to multiply the whole right side?
not just the part your doing
so if i did multiply into n what would that solution look like
could i get that equal to the correct answer
slim cove
yep you have to multiply the m to the wholeee right side
you should be able to get that into the correct answer yea, I haven't tried tho
vague mural
im gonna try, if i get a different answer ill regroup here and crank ur neck another 90*
slim cove
kk
vague mural
i tried turning my camera i think i made it worse
um yeah but i didnt get the right answer
my guess is when i divided the left side by 50 and m something went wrong
,rotate
warm shaleBOT
vague mural
W moment
slim cove
hmm
oh okay
yeah you can't split up the fraction like that
it should be that $$\frac{Lm - 125}{50m} = \frac{Lm}{50m} - \frac{125}{50m} = \frac{L}{50} - \frac{5}{2m}$$
warm shaleBOT
Eric Tao
slim cove
does that make sense?
slim cove
👍
vague mural
the dividing 50 off n and m off n is weird
why would you combine them afterward
i thought u might need to do LM-125/50/m
slim cove
wait sorry which step are you talking about
slim cove
so do you mean when we had $$Lm - 125 = 50nm$$
warm shaleBOT
Eric Tao
slim cove
and we divided 50m
vague mural
would stuff/50/m still be the same as stuff/50m
slim cove
first divide by 50
yep!
so (stuff/50)/m is the same as (stuff/m)/50 which is the same as stuff/(50m)
vague mural
which would you do first of the division sets
slim cove
it doesn't matter
you can divide by 50 first and m second
or you can divide by m first and 50 second
the beauty of math is that it all works out :)
vague mural
but at the end of the day wouldnt 50m have multiplication so its not the same as dividing by m or 50?
like litterally the fact it has multiplication in it
slim cove
let me show you with some numbers
slim cove
so you agree that $$24 = 2\cdot3\cdot4$$ right
warm shaleBOT
Eric Tao
vague mural
yes
slim cove
okay so let's try all three methods we discussed before
vague mural
alr
slim cove
so let's try dividing by 2 and then dividing by 4
then $$12 = 3\cdot4$$ and $$3 = 3$$ so it all works out perfectly fine
vague mural
24 dividing that by 2 and 4?
warm shaleBOT
Eric Tao
vague mural
wait so
this shows after 24/2
huh
can you show the whole equation of ur example?
ohhhhhhh
so its just bringing that up to eachother
slim cove
yep so like we can also divide by both 2 and 4 at the same time
vague mural
man thats wild
slim cove
so if we do $$\frac{24}{2\cdot4} = \frac{2 \cdot 3 \cdot 4}{2\cdot4}$$ then we get $$\frac{24}{8} = 3$$ which is also correct!
math is so wild!!
warm shaleBOT
Eric Tao
vague mural
thats hard to wrap my mind arround and normally i wouldnt belive it but numbers indeed dont lie
slim cove
it can take time :)
it's very cool though
dividing by (two numbers multiplied together) is the same as dividing by both of them separately
vague mural
oh and thats because you do (stuff)/(stuff2)?
slim cove
hahahaha
vague mural
this stuff is so cool
vague mural
yeah i got college after this year
so hopefully every1 else also didnt focus about anything in school
now is my time to get ahead
slim cove
yes! good luck mate
obtuse pebbleBOT
light sand
Can I have help in 3
obtuse pebbleBOT
Available help channel!
near grail
Help me pls someone
obtuse pebbleBOT
Help me pls someone
primal wadi
Help me pls someone
the 2 arrow means parallel right?
near grail
Yeah
near grail
Nope
primal wadi
i see
wooden cipher
i think a better question is do you know what b is?
primal wadi
what laws do you know for parallel lines
near grail
I think it asking both
primal wadi
what laws do you know for parallel lines
in terms of angles
near grail
I think so
wooden cipher
well yeah, but we can start with whichever is easier, and b is easier
near grail
Ok then b it is
primal wadi
well yeah, but we can start with whichever is easier, and b is easier
is it? a is just a+ 56=180
primal wadi
do you not need it for a as well
you dont
a+56=180 for parallel lines
no need to deal with right angles
primal wadi
this is the 3 things you need to remember @near grail
near grail
a+56=180
a=180-56
a=123
wooden cipher
try that calculation again
near grail
??
wooden cipher
180-56
near grail
I used a calculator
wooden cipher
??
near grail
It says 124
wooden cipher
there you go
wooden cipher
no need to deal with right angles
using this diagaram, what type of angle pair would be useful to find it?
near grail
Interior?
wooden cipher
err not quite
corresponding is more useful
since we know the corresponding angles
near grail
??
wooden cipher
<BAE corresponds with <DCE
near grail
Corresponding angle can be used to find b?
wooden cipher
i thought we are looking for the top one right now
near grail
b+90+56=180
wooden cipher
well yeah
wooden cipher
yeah you already found a and b is set up
near grail
How do I find a??
wooden cipher
a+56=180
a=180-56
a=123
you did it right here
wooden cipher
<BAE corresponds with <DCE
do you understand what i meant when i said this?
wooden cipher
corresponding angles have the same value, do you get that part?
near grail
Yeah
wooden cipher
if i cut your photo like this, does it look like the diagram that qwerty sent?
wooden cipher
the two angles correspond as well
near grail
So the top is 90?
wooden cipher
yup
near grail
But why don't they mark it down on the book
wooden cipher
otherwise its easier to find b
since you can just look at the triangle ABE and find the other angle
near grail
a=34?
wooden cipher
yes
near grail
Now this one I really don't know how to do it
near grail
Yeah it very hard to see it
wooden cipher
do you know which property of parallel lines we can use here?
near grail
Next to 3c
wooden cipher
heres the image
near grail
Corresponding
wooden cipher
ah not quite
near grail
Alternate?
wooden cipher
actually its interior
near grail
Ok
near grail
Yeah I see it now
wooden cipher
so what is the value of c
near grail
3c+4c=5c
wooden cipher
you have to be a little more specific
interior angles are different from the other two
so its not that one equals the other
they sum to 180
wooden cipher
yes
near grail
Hold up let me ask me teacher if I learned this in the first term
wooden cipher
if you dont mind me asking, wht country do live in
near grail
You first
wooden cipher
it kinda struck me that youre asking the teacher late at night in the US lol
wooden cipher
ah got it
near grail
But I'm not fully Chinese
Just some guy at 3 am ask his teacher will this one question be in the exam
Let's just continue
near grail
12c?
wooden cipher
12c=?
near grail
180
wooden cipher
alright, so c=?
near grail
Right?
wooden cipher
yes
near grail
168????
wooden cipher
that is c+12
we need 12c=180
near grail
15
wooden cipher
yup!
near grail
Wut!!
wooden cipher
so now we need to figure out d
near grail
wooden cipher
that is c+12
we need 12c=180
for this remember we have to divide not subtract
near grail
Alright give me a sec to write it down
wooden cipher
ok
near grail
Done
wooden cipher
ok so now we need d
near grail
@wooden cipher do you play any games??
wooden cipher
like board games, fps, chess?
near grail
Mobile
near grail
You wanna add me??
wooden cipher
anyway can we finish the problem
near grail
Ok
near grail
d+2d+15=180
near grail
wooden cipher
we actually know that BCD is a straight line so lets use that
ill do that later
im on laptop rn
near grail
Ok
wooden cipher
so BCD is a straight line, how can we use that to find ACB?
can we finish the problem please
near grail
Ok
Just in case you fall asleep on your laptop
BCD is a straight line
Hmmmmm
How do we find the top of D
wooden cipher
what is the value of c?
daring steppe
What are we solving for?
near grail
wooden cipher
we are trying to solve for d
proven zephyr
the top pic?
near grail
Top one
proven zephyr
ok so you already got c
near grail
Yeah
proven zephyr
what
daring steppe
Sorry if this is a stupid question, but how do you know 3c + 4c +5c = 180
near grail
@wooden cipher told me
daring steppe
Uhhhh
proven zephyr
so you dont understand?
near grail
Sorry if this is a stupid question, but how do you know 3c + 4c +5c = 180
I do for this one
proven zephyr
do you know how the top D's angle is 3c?
near grail
Really??
proven zephyr
wait you dont know that?
near grail
Nope
proven zephyr
so.. you dont understand how you got 3c + 4c +5c = 180
near grail
So it's
d+2d+3c=180
near grail
so.. you dont understand how you got 3c + 4c +5c = 180
I do
proven zephyr
So it's
d+2d+3c=180
no?
proven zephyr
BCD is a straight line and angle ACD is given
near grail
Uhh huh
proven zephyr
ok lemme just give you an example
near grail
Ok I like examples
near grail
180-60
proven zephyr
yes
near grail
120
near grail
near grail
x+3+15=180
proven zephyr
x+3+15=180
where did you get 15..
near grail
C=15
proven zephyr
ok you might want to do the algebra course in the app you have
near grail
Can you give me the set up??
daring steppe
Yeah the set up is above
daring steppe
This
near grail
near grail
Yeah
proven zephyr
no they're not
near grail
....
daring steppe
Ok, just generalize it, imagine instead of 60, there was any angle, next to x. If 180 is the entire thing and 3c is the part we DONT want. What is x
near grail
c?
daring steppe
Uhh
Not exactly
It’s 180-3c
You should be able to do it yourself, but do you at least understand why?
near grail
Oh yeah
daring steppe
Ok
near grail
After this one I'm gonna eat
daring steppe
Can you solve for x?
near grail
x=180-6y
near grail
Yeah
proven zephyr
additional information:
daring steppe
Solve x
daring steppe
Good! Simplify!
near grail
well my teacher that one letter is 1
daring steppe
?
near grail
Nvm
daring steppe
So what does it simplify to?
near grail
x=178
daring steppe
d is not equal to 1
daring steppe
Ok, so I want to know your thought process. Why do you think x=178
daring steppe
That’s not how variables work
near grail
Oh
daring steppe
You can’t just set a variable equal to 1
You need to find x in terms of d
Just like we did before with c and y
near grail
daring steppe
Do you understand? I can go over it again
near grail
Yes pls
daring steppe
I think you need a bit more help with fundamental algebra than geometry though
Ok if I said x+y=180
How would you solve for x?
near grail
x=180-y
near grail
Yeah
daring steppe
So d+2d+x=180 right?
near grail
Yeah
near grail
x=180-2d-d
daring steppe
Correct. Can you simplify that?
near grail
Idk how do I just subtract 2 from 180??
near grail
5x
daring steppe
Ok now simplify 180-2d-d
near grail
178d
near grail
180-(2d+d)
near grail
daring steppe
Ok so do you understand everything so far?
near grail
Yeah....
near grail
3d and 3c??
daring steppe
Well yea. But what equations can you make, given a straight line is 180 degrees
near grail
180-3d-3c
daring steppe
You might want to check your work on that, it is very close
near grail
180-6d-3c
daring steppe
Where did you get 6d from
near grail
d+2d+3d
daring steppe
Where did you get 3d from
near grail
daring steppe
That says minus 3d, you can’t just ignore the sign
near grail
Ohhhh
daring steppe
Do you see it
near grail
I do now that you mentioned it
daring steppe
Now this is simple algebra
Can you find a relationship between c and d
?
Using this formula
near grail
One's plus and one's minus??
daring steppe
Well yes. But can you solve for d in terms of c
Just like before with x and c and y
near grail
I'm gonna eat my food real quick
daring steppe
Ok
near grail
Will u still be here?
daring steppe
Yes
near grail
Ok thanks
daring steppe
daring steppe
Yes
Ok so, 180-3d+3c=180
Solve d in terms of c
Just like before with x and c and 6y
near grail
3d=180-180+3c
near grail
3d=3c
daring steppe
What happened to the c?
You can’t just stop using variables, they must stay through the entire equation
Oh ok
So now
What can you conclude about c and d
near grail
d=3c÷3
daring steppe
Yes
near grail
d=1c
daring steppe
So c=d! Right?
near grail
Yeah
daring steppe
what do you mean by that
daring steppe
Yes
near grail
Ok
daring steppe
I have to go, I hope you understand now! Bye!
near grail
Thanks for your help
daring steppe
No problem!
near grail
.close
dim rock
Guys someone explain me whats happening in this
obtuse pebbleBOT
Guys someone explain me whats happening in this
@dim rock Has your question been resolved?
versed gale
$\sum_{i = b}^{a} p_i$
obtuse pebbleBOT
$\sum_{i = b}^{a} p_i$
warm shaleBOT
alijfri99
versed gale
Suppose a summation like this where b is less than a
Does this summation evaluate to zero or is it undefined?
oblique light
Think of it like code
oblique light
,w Σ_(n=5)^3 n
warm shaleBOT
versed gale
But maybe that's how the code to that program was written?
As in, it creates an initial variable with value zero and then runs a for loop and returns the variable in the end, but the for loop never runs in this case and so zero is returned?
oblique light
i = b;
sum = 0;
while (i<=a):
sum += p_i;
i++
print(sum)
Yeah thats basically exactly what the sigma notation does as well
It is code
versed gale
Yeah I did think of it in terms of loops too, but I thought maybe this one is a special case in math
oblique light
0 has a special meaning here
Zero is the additive identity, and is equal to the sum of no addends
1 is the multiplicative identity, and is equal to the product of no factors
versed gale
True
oblique light
In more advanced contexts we actually forgo this summation over integers with upper and lower bounds and can just sum over sets of elements
So let's rewrite your sum as a set
$\sum\limits_{i \in \mathbb{Z} : {b \leq i \leq a}} p_i$
Please format correctly
warm shaleBOT
AMD
versed gale
Actually, I was going to say
This happened as part of an induction problem
kekw
I think the problem with the false induction proof is that P(0) does not imply P(1)
oblique light
Lmao
What exactly are we summing
What is P(0)
2+3+4+...0
Ah now your question makes sense
versed gale
$\sum_{i = 2}^{n} i$
warm shaleBOT
alijfri99
versed gale
But yeah P(1) is zero
oblique light
Yeah I think this is it, faulty base case
versed gale
The base case is actually correct I think
More like it's a missing link in the chain of implications
oblique light
Wait actually, P(1)=0 using our summation, but P(1) = 1 using the derived formula
versed gale
Yeah that too
I think that's the same thing logically
is it though
Yeah it is
P(1) is saying that 0 = 1
So it's false
But P(0) is true
So P(0) -> P(1) is in the form T -> F
Therefore it's false
oblique light
Yes
oblique light
I would say that it's more sleight of hand than anything
This is a magic trick
A well-designed one I'll admit
versed gale
What are you referring to?
oblique light
Specifically the way in which the expression:
2+3+4+....+n
is treated
versed gale
yeah I agree
the textbook actually warns against writing '...' in such situations, as it says that it can be a source of errors.
There are also some other funny induction proofs in the chapter with pretty much the same flaw, for example one that says all horses are the same color.
oblique light
Yeah that's a classic
oblique light
versed gale
.close
timber lark
How do i do this? I tried a lot of ways, but i end up with difficult numbers
royal basin
and what difficult numbers are you ending up with exactly
royal basin
what are you trying to calculate here?
timber lark
X and Y
royal basin
what?
timber lark
When you want “x” your turn “y” into 0
royal basin
did you maybe mean the x-intercepts and y-intercepts?
timber lark
Yeah
royal basin
calling it "the x" is disingenuous.
so you were trying to calculate the x-intercepts...
timber lark
Yeah
royal basin
well, you should not have gotten sqrt(-13/2).
timber lark
I know, i cant figure out why
royal basin
if anything, you should have gotten to (x-2)^2 = -1/3
did you get to (x-2)^2 = -1/3?
timber lark
No
royal basin
then show your work.
royal basin
,rccw
warm shaleBOT
royal basin
(x-2)^2 ≠ x^2 + 4.
while the correct expansion would've been x^2 - 4x + 4, you in fact do not need that here.
royal basin
well i would subtract 1 from both sides to get 3(x-2)^2 = -1 and then divide both sides by 3 to get (x-2)^2 = -1/3
and then say that squares are never negative, so this equation has no (real) solutions.
and your parabola does not have any x-intercepts.
timber lark
Oh ok
atomic hornet
Are you being asked to plot this function?
timber lark
Yeah
atomic hornet
Are you familiar with graph transformations?
timber lark
Yeah
atomic hornet
Well, you could just imagine y=x^2 and transform it
atomic hornet
The +1 is correct, but why have you moved it 3 to the left?
timber lark
Oh, is it to the right?
atomic hornet
A transformation of 3f(x) would do… what?
timber lark
Oh i thought the y=“3”(x-2)^2+1 meant it moved left
atomic hornet
f(x+a) would move the curve horizontally, af(x) would stretch the curve vertically
timber lark
Ok
atomic hornet
So with that in mind, try sketching again
wanton dagger
How could I do this question?
obtuse pebbleBOT
How could I do this question?
lofty jay
hint: try to express the sin on the lhs in terms of a cos
knotty crow
How could I do this question?
u can use cos(A-B) then simplify
wanton dagger
Ok
lofty jay
thatd be more complicated
wanton dagger
Yh
timid silo
hint : sinb=cos(90-b)
timid silo
How could I do this question?
do u have some domain restrictions?
wanton dagger
Nope
wanton dagger
hint : sinb=cos(90-b)
How could I use this here?
lofty jay
rewrite the lhs
wanton dagger
Cos(90-b)=cos(2b-30)?
timid silo
yes
timid silo
be careful here coz cos isn't injective
wanton dagger
What do you mean by that?
timid silo
I want to say
that
cos(a)=cos(b)
doesn't necessarly nake
a=b
it has infite solutions
wanton dagger
Oh
wanton dagger
I see
For example in quadrant 4 another solution would be 320 degrees
Ok makes sense now
wanton dagger
?
timid silo
use the fact that cos(360-x)=cos(x)
wanton dagger
Ok
timid silo
then it will be more clear
obtuse hatch
obtuse pebbleBOT
fickle turret
What have you tried so far?
obtuse hatch
i did 5 to the power of 5 but i dont think its right
fickle turret
"with no repetition"
light sand
Hi
hexed agate
obtuse pebbleBOT
@light sand Has your question been resolved?
plucky patio
Can anyone identify where I’m going wrong? I plugged the question in an online calculator and I’m getting a different answer
obtuse pebbleBOT
Can anyone identify where I’m going wrong? I plugged the question in an online c...
timid silo
c is a constante right?
plucky patio
You mean +c?
timid silo
yep
plucky patio
Idk that’s just smth you add in when you integrate
plucky patio
yes
timid silo
$\cos^2(x)=(1+cos(2x))/2$
warm shaleBOT
seif
timid silo
u have this too
plucky patio
I have an extra 3/2
plucky patio
show me the first line
the question?
timid silo
the question?
yes
plucky patio
timid silo
The answer you get $2x-\sin(2x)-\frac{3\cos(2x)}{2}+C$ is totally correct. You just need to use some identities to make the $\cos(2x)$ term becomes the form you want.
warm shaleBOT
bad at maths
timid silo
Hint: $\cos(2x)=2\cos^2(x)-1$
warm shaleBOT
bad at maths
obtuse pebbleBOT
@plucky patio Has your question been resolved?
plucky patio
Yes, but this is what I got when I tried to rewrite the part that didn't correspond
ashen seal
Got this question "Find the number of degrees in the acute angle formed by a tangent through one vertex and an adjacent side of an inscribed a) square; b) equilateral triangle; c) ... ". But I'm stuck at trying to draw this question on paper, can't decypher what they mean.
obtuse pebbleBOT
Got this question "Find the number of degrees in the acute angle formed by a tan...
boreal dew
https://cdn.discordapp.com/attachments/912123250455232543/992776931885985822/Screenshot_20220702-140052_Drive.jpg hi sorry this is my first post here, I do not understand how to solve part (a), in particular, relating Theta to the new sizes r and h.
obtuse pebbleBOT
https://cdn.discordapp.com/attachments/912123250455232543/992776931885985822/Scr...
boreal dew
by substitution: r = R(1-gamma) and h = R * \sqrt(2gamma - gamma^2)
but i have no clue how to get from a 2D disc to the 3D cone by merging the sides together
nevermind i found it you have to correlate the initial area of the circle to the size area of the cone
.close
weak belfry
obtuse pebbleBOT
weak belfry
Hi everyone, so I've found 2 values that sin x can be
however the answer only states 1/3
tranquil arch
the range of sin(x) is [-1,1]
solemn ravine
sin(x) = 5/2 implies x is complex and i am guessing you are working over the reals
weak belfry
cus it only go up to 1
solemn ravine
o someone already answered
weak belfry
what does x is complex mean
pine sail
It means, there aren't any real values of x that satisfy your problem.
solemn ravine
the answer to that question requires quite a bit of explanation
weak belfry
so what would a not real value be like
solemn ravine
it has to do with that blue guy's profile picture
pine sail
so what would a **not real** value be like
A complex one.
pine sail
For real numbers, yes it doesn't.
solemn ravine
IT DOES WORK just not for your purposes
solemn ravine
nothing (: u will get to a stage where u will understand soon
solemn ravine
🥲
weak belfry
bruv
pine sail
Depends.
weak belfry
just formula and equation
weak belfry
well this stuff is in further maths A level
o
pine sail
I mean you will get to know complex numbers before uni, just the basics but yes.
solemn ravine
do you do further maths?
weak belfry
there was a chapter called complex number
solemn ravine
like, theres maths A level and theres further maths A level
its like a separate A level
solemn ravine
yeah then you wont learn complex numbers i think
pine sail
“How am I to know which solution to take and which one not to?"
In case you wish to know that, watch some basic trig videos to know the range for trigonometric functions.