#help-23
flat frigateBOT
\[ \lambda \]
opaque sorrel
how thou
toxic stratus
but like you'd assume the problem set has nice polynomials
so that you can actually solve for lambda by hand
toxic stratus
use like the lagrange expansion or whatever it was called
or was it cauchy
too many famous math people
opaque sorrel
too many famous math people
snow is one of them
toxic stratus
opaque sorrel
opaque sorrel
<https://en.wikipedia.org/wiki/Laplace_expansion>
OH that
o yeah
speaking of which
toxic stratus
i think A - λ might be easier ngl
opaque sorrel
computing matrix multiplication is
toxic stratus
then you dont have to invert A
opaque sorrel
O(n^3) right
toxic stratus
no i dont think thats a good idea
plucky elk
at least for j) it's a permutation matrix so its eigenvalues are roots of unity.
opaque sorrel
whats a permutation matrix
toxic stratus
matrix which permutes the coordinates
opaque sorrel
,w determinant ((x + 1, x), (2, x))
flat frigateBOT
flat frigateBOT
opaque sorrel
whoever made wolfram is goated
@toxic stratus sad
the answers wrong
oh wait
do i need to
factorize it
toxic stratus
that looks like a different question 
opaque sorrel
,w factorize x^3 - x^2 - x + 1
flat frigateBOT
opaque sorrel
o
ah wait
its different
oops
im confused
oh wait
lmao
this is
part h
flat frigateBOT
toxic stratus
solve for the roots
opaque sorrel
x = 1 and x = -1?
toxic stratus
ye
flat frigateBOT
toxic stratus
so if you rearrange that
flat frigateBOT
toxic stratus
the nullspace are just the vectors which satisfy that equation
flat frigateBOT
toxic stratus
in a sense yeah
opaque sorrel
o!!?!?!?
flat frigateBOT
opaque sorrel
now
i want to find
the basis
for eigenspooces
so
each eigenvalue
has a unique eigenspace
ok
so
man so many terms
so conufisng
toxic stratus
mm
toxic stratus
yeah
i think its probably easier to do A - lambda tbh
cuz then you dont have to negate the whole A
opaque sorrel
and this is because the eigenspace is in the nullspace of I - A
toxic stratus
less error prone
flat frigateBOT
flat frigateBOT
toxic stratus
its just like your usual gaussian elim stuff
opaque sorrel
its just like your usual gaussian elim stuff
toxic stratus
yeah i guess so
opaque sorrel
o
wait
lemme recap
so like
lambda is 1 which is an eigenvalue
then i want to find the line/plane/etc of that lambda
which is the eigenspace
toxic stratus
yeah
opaque sorrel
then i want to find the line/plane/etc of that lambda
such that Av = lambdaIv
toxic stratus
yes
opaque sorrel
o
okay
now
so
to solve for that
i equate A - lambdaI
i mean find
and this charactertisctic polyoasmisaal
what would it represent
toxic stratus
the characteristic polynomial is how you get the eigenvalues in the first place
but to find the eigenspace corresponding to an eigenvalue you solve (A - λΙ)v = 0
opaque sorrel
hm
so like
now ive found the matrix representing the cahracterstic aspdolymonaiamla
and RREFED it
so like
wait sorry but like
what does that matrix represent
toxic stratus
like
flat frigateBOT
toxic stratus
so then after you row reduce
opaque sorrel
oh wait
OHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
ill get the vectors
like the usual x y and z
flat frigateBOT
flat frigateBOT
toxic stratus
yes that v
opaque sorrel
so two arbtityrrary values
toxic stratus
so say you set $v_2 = s$, $v_3 = t$
flat frigateBOT
opaque sorrel
yes
toxic stratus
then in this equation
flat frigateBOT
toxic stratus
which means for v
flat frigateBOT
opaque sorrel
then we jjust multiplied it by 2
toxic stratus
yeah
toxic stratus
lean otter
If I have $40 and it's 4cents per megabyte, how many gigabytes do I have? (im not dumb i just dont know how to solve it, im 13 dont judge plz)
safe radishBOT
If I have $40 and it's 4cents per megabyte, how many gigabytes do I have? (im no...
stray bluff
how many megabytes in a gigabyte
lean otter
1000
foggy salmon
1024
lean otter
fuck
foggy salmon
hm
lean otter
maybe i am stupid
foggy salmon
na idk
lean otter
wait nvm its 1024
foggy salmon
yes
lean otter
its just most people like 1000
foggy salmon
LOL
stray bluff
my question was for the context of this problem is it 1000 or 1024
stray bluff
does it specify @lean otter
thin crow
in reality its 1000
foggy salmon
D:
lean otter
just go with 1k
thin crow
ur getting 1000
foggy salmon
is this a cs subj or math
lean otter
yes
thin crow
ye
40 / 0.04
0.04 because thats 4 cents
1 dollar = 100 cents
40 / 0.04 is 1000
thats 1000 megabytes
so 1 gb
lean otter
im getting 1gb?
thin crow
yea
stray bluff
Whats so incorrect about it
thin crow
it is correct
stray bluff
yes
thin crow
??
stray bluff
Is this like for a class or a real life thing?
lean otter
real life
thin crow
same thing with 4
stray bluff
why u paying 0.04 per MB
lean otter
its a starter kit simcard
i can go with this which expires in 1 year
or i can go with expire in 1 month but i get moer
stray bluff
idk where u live but I pay like $0.001 / MB
lean otter
i live australia
stray bluff
🤷♂️
stray bluff
urm idk this isnt really a math problem lol
lean otter
ik but 😃
thin crow
js go w the first one
lean otter
aight
ill just buy a new sim in a month
or maybe i can recharge or smth
ill have to read the tos
thanks guys
.close
lean otter
Just wondering if I did this right T_T, I feel off with it but idk what
lean otter
Testing absolute convergence test for alternating series also
Where did the 1/n^2 come from to begin with?
Uhhhh I was trying to compare to a p series, that’s where I felt off tbh
Are you trying to use limit comparison with alternating series test?
Yus
You just need to do the alternating series and see if the sequence of that goes to 0
clear blade
lean otter
Yea that
Ohhh okay, this question was on an absolute convergence test handout with the possibility of using alternating series test
The alternating series test doesn't help to prove absolute convergence
clear blade
for absolute convergence, you need to test the series without the alternating part
lean otter
Ratio test is a good shot
Ohhh okay, I thought I did that by just taking 2n+9/n^3+1 and testing it with the limit comparison test mb
clear blade
Ohhh okay, I thought I did that by just taking 2n+9/n^3+1 and testing it with th...
your proof is correct
i didn't realize you were testing absolute convergence using the limit comparison test
what do you mean "no info?"
lean otter
Well since my P was greater than 1, doesn’t that mean that my series diverges, and in the absolute convergence test, you don’t get any info from doing that, right?
clear blade
lean otter
So it converges then
clear blade
yes
surreal sorrel
Should I proof by contradiction or direct proof both?
safe radishBOT
Should I proof by contradiction or direct proof both?
surreal sorrel
$O(2^{n})=22n^{2}+19n-63$
$O(3^{n})\neq 19n^{2}+63n-22$
queen bluff
hard canopy
im new
Read #❓how-to-get-help please
lean otter
okay
drowsy moss
take that skynet!
surreal sorrel
Thinking of using limits, but direct proof or contradiction seem simpler
(1) Nope. Doing direct proof. Choose k=1 assuming n > 1 thus n^2+2n+1 is O(n^2) because n^2+2n+1 <= 4n^2 whenever n > 1
surreal sorrel
Now it should be good. Does this satisfy the proof?
Ah bogus, the given constants do matter...
safe radishBOT
@surreal sorrel Has your question been resolved?
safe radishBOT
@surreal sorrel Has your question been resolved?
safe radishBOT
@surreal sorrel Has your question been resolved?
digital crane
how do i simplify this
digital crane
safe radishBOT
@digital crane Has your question been resolved?
lean otter
safe radishBOT
lean otter
do I need to transform the sqrt into an exponent?
and does 1 / x ^ 1/2 have an equivalent in a form that isn't a fraction ?
halcyon carbon
x^(-1/2)
wicked jewel
safe radishBOT
wicked jewel
Hey I am having difficulties with solving this, I thought that I was on the right track but it seems I was wrong
Here's what I tried doing
quasi bison
this is not a geometric series...
wicked jewel
Oh I see that now, I've been thought that I should trat it as one
quasi bison
also are you sure you copied the original problem statement correctly? because as-is, taking the sum wrt n and then the limit wrt n doesn't make sense symbolically
wicked jewel
Find the sum of the row:
quasi bison
this is a long shot but do you happen to be Russian
wicked jewel
no
quasi bison
okay nevermind
wicked jewel
How did you deduct that?
quasi bison
it's just that in english the word for an infinite sum is "series"
but "row" is a common mistranslation of the Russian ряд
wicked jewel
My first language is not English and we study math in our language in uni
Sorry for any inconveniences that this may cause
quasi bison
anyway
quasi bison
so you need to find the sum of this series
wicked jewel
so you need to find the sum of this series
Yes, I need Sn
lean otter
Oh I see
wicked jewel
And the answer is what the limit of Sn is
However I am oblivious as to how I can do that
quasi bison
i'm not sure the partial sums have any nice expression here
worth a try though
hold on
,w partial fractions n/(n^2-4)^2
wicked jewel
We've been told to do it using partial sums so I believe that's the way to go
flat frigateBOT
quasi bison
right, so it looks like you are in luck
wicked jewel
Do you just want to prove if it is convergent or find the sum?
just the sum
what does convergent mean?
lean otter
Hm was gonna say the integral test may be handy here
quasi bison
$S_n = \sum_{k=3}^n \frac{k}{(k^2 -4)^2}$ and when you write this out using the partial fraction decomposition from WA you get a lot of stuff canceling out
lean otter
But
flat frigateBOT
Ann
lean otter
Oh yeah partial fractions, forgot those for a second
lean otter
what does convergent mean?
The series has a finite sum
quasi bison
what does convergent mean?
convergent series = сходящ ред
i have not taken any steps yet
wicked jewel
convergent series = сходящ ред
okay so it means what I thought
from where did u translate it?
quasi bison
only written out more explicitly the nth partial sum to not get caught up in symbol bullshit
quasi bison
from where did u translate it?
looked up the article for infinite series on Wikipedia
wicked jewel
dope
quasi bison
some terminology is fairly similar between Bulgarian and Russian
wicked jewel
yeah that as well
but it's different in English, or it might not be but it's different and harder to grasp
quasi bison
anyway, WA says k/(k^2-4)^2 = 1/8 (1/(k-2)^2 - 1/(k+2)^2)
so when you write the sum of this for k from 3 to n, you get... i think four terms at the start and four at the end that don't cancel
but everything else annihilates
wicked jewel
anyway, WA says k/(k^2-4)^2 = 1/8 (1/(k-2)^2 - 1/(k+2)^2)
I need the steps as to how it got to getting to this
lean otter
🔭?
wicked jewel
Because that's the part that I need to learn
quasi bison
it's called "partial fraction decomposition" in english
i can't find the Bulgarian term but it's probably something like частични дроби
wicked jewel
Okay, I found which methods we are supposed to do it with
I think we are supposed to use uhh
criteria of Gauss
lean otter
i can't find the Bulgarian term but it's probably something like частични дроби
Maybe saying it in Russian could be helpful as the two languages have some similarities
wicked jewel
it's called "partial fraction decomposition" in english
I understand it from what it's like rn
I don't get why they are using Gauss's Law isn't it only for proving if it's convergant
wicked jewel
then idk why my colleagues solved it using Gauss' criterion
we have to find the sum not the type
median sphinx
safe radishBOT
median sphinx
The lst one is 2020C2020
safe radishBOT
@median sphinx Has your question been resolved?
safe radishBOT
@median sphinx Has your question been resolved?
ember bolt
Guys I need help
safe radishBOT
Guys I need help
ember bolt
How to prove 10 and 12
With double angle formulae and compound angle formulae
pls show steps so that I will understand
.close
safe radishBOT
fluid holly
Aight
safe radishBOT
Available help channel!
knotty pumice
Can I send my thing here?
safe radishBOT
Can I send my thing here?
fluid holly
Yes
knotty pumice
Apparently this is incorrect for make X the subject and I don’t get how
fluid holly
Is the question right?
knotty pumice
Yes
steep pewter
u need to get x?
knotty pumice
There’s an answer box for the homework and it’s not on there at all and I don’t what I did wrong
knotty pumice
u need to get x?
Yes
knotty pumice
But isn’t that the same as what I did?
Ig mine ain’t very simple and probaly wrong but still
.close
safe radishBOT
fluid holly
knotty pumice
Ok thanks
steep pewter
welcome
safe radishBOT
Available help channel!
kind roost
I need help regarding circles
safe radishBOT
I need help regarding circles
lean otter
What regarding circles?
kind roost
flat frigateBOT
3317
kind roost
**3317**
Oh damn wait i completely forgot about that theorem
Well damn thank you
Wait is it a theorem?
stray socket
It's a theorem that stems from vertical angle propertoes
harsh pine
Let a,b in R and 0 < a <= b.
safe radishBOT
Let `a,b in R` and `0 < a <= b`.
flat frigateBOT
madmike
harsh pine
I somehow need to simplify this to a <= b I think
keen comet
that looks like a wrong direction or goal to me
keen comet
Can't comment about the other parts
keen comet
**madmike**
But this one should be proven with an alternative goal
keen comet
Go back to $2ab \leq a^2 + b^2$
flat frigateBOT
草w
keen comet
Stare at it harder.
harsh pine
in my mind I tried dividing by 2 but that doesn't help
bringing something to another side doesn't seem to help
dividing by ab doesn't work because there's a sum on the other side
or maybe 
flat frigateBOT
草w
keen comet
**草w**
Other than that, this is literally the answer
Graph it on desmos or something
maybe you'll see it
keen comet
In your working you want to write $ab \neq 0$ as justification
This is true by the question primitives/assumptions, so it's not an issue
median sphinx
cant u jut do 0 <= (a-b)^2
bcs that prove that the number in (a-b)^2 will always >= 0
0 \leq a^2 - 2ab + b^2$
$0 \leq a^2 - 2ab + b^2$
@harsh pine
oo nvm, i think it cant solve ur question
harsh pine
This can't be so hard
it's a beginner math course
I need a hint
If I arrive at ab != 0, why is the inequality proven?
because ab != 0 is true from the question assumptions?
but $2ab <= a^2 + b^2$ is true even for $a=0$ and $b=0$
flat frigateBOT
madmike
harsh pine
I don't understand
This doesn't seem correct
by the way I am stuck on a different exercise at exactly the same point
toxic stratus
bruh
just because your implications technically go both ways
doesnt mean you should write all of your working backwards
this is very bad writing
harsh pine
how do you start?
toxic stratus
you start from somewhere which is generally accepted to be true
and then you write your steps
and reach the conclusion
here you're assuming the conclusion
and arriving at wherever
but it doesnt matter where you arrive at because you already assumed the conclusion
harsh pine
lol I see
toxic stratus
its like saying assume 1 = 2 so blah blah blah so 1 = 2
harsh pine
so I start with a <= b
because that's the assumption from the exercise
and then try to arrive at this?
harsh pine
I am a bit confused because I have "nothing to work with" if I start with "a <= b"
$\Leftrightarrow 2ab \leq 2b^2$
flat frigateBOT
madmike
harsh pine
This is not the same as what I had up there with 2ab <= a^2 + b^2
toxic stratus
like
flat frigateBOT
harsh pine
this is what I did 
flat frigateBOT
toxic stratus
no this is a direct computation
you dont start by writing down the result
you start from somewhere wherever it may be and then arrive at the result through a sequence of logical steps
harsh pine
is there a reason you use => instead of <=>?
should I favour => too?
because we only care about 1 direction?
toxic stratus
the implication goes both ways but you're only proving one direction
harsh pine
also I am not sure where you get the idea from to start with (1 - x)^2 >= 0
toxic stratus
you must be sure that the implication goes both ways before you write <=>
you start with (1 - x)^2 >= 0 after working it out
you write your rough working elsewhere
from which you will discover that is what you need
and then you rewrite your proof in the logical order
harsh pine
Could you tell me how you would start to prove this?
toxic stratus
think about the example i showed you
toxic stratus
its remarkably similar to the step you're stuck on
flat frigateBOT
harsh pine
idk I just can't wrap my head around how to get to the desired result
wait that's wrong
what am I writing
🤔
but that's not the same as this
toxic stratus
how do you get (a + b)^2
toxic stratus
how do you create a (a + b)^2 in here
toxic stratus
bot ded
uh
if you rewrite the inequality ab <= ((a + b)/2)^2 you get 4ab <= (a + b)^2
this is not what you have here
you need the 4ab
safe radishBOT
@harsh pine Has your question been resolved?
keen pebble
I need some help lmao
safe radishBOT
I need some help lmao
keen pebble
Anybody there?
split ether
Don't ask if there's anybody to help, just post the question
keen pebble
Alright
So my task is to find out how high the water is after 10 minutes with the equation 16/1 t^2-5t+100= 50
The graph is like a parable
keen pebble
Is that a thing i have to see in order to solve this one?
stray socket
No it legit like
Gives you what to plug in
"find how high the water is after 10 minutes"
keen pebble
So just put in 10 as t
stray socket
Yes
keen pebble
Wow
stray socket
The question literally spoonfeeds you how to solve it lol
You pray for these questions lol
keen pebble
Bro its late💀
keen pebble
You pray for these questions lol
💀
Thatll be some hard years
Is there any way i can get a mathematic eye like that
stray bluff
practice
stray socket
Practice
keen pebble
I do but i still dont have that tranlation in my head of what they want from me when they wrap these questions up like that
Like they want me to solve how much waters been drained after 10 minutes
Is it like the average rate of it draining away @stray socket
safe radishBOT
@keen pebble Has your question been resolved?
flat frigateBOT
madmike
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
safe radishBOT
@keen pebble Has your question been resolved?
safe radishBOT
@keen pebble Has your question been resolved?
keen pebble
How do i solve x^2-3a+2a^3 ??
safe radishBOT
@keen pebble Has your question been resolved?
swift palm
Is that separate from your earlier question?
idle tiger
claim
idle tiger
How is the answer D in this question? I understand that it needs to be divisible by 4 so the last two terms of each function should = 0. But why can’t It be C also.
final halo
C is a special case of D
C does not have to be true in general, the two x³ terms just have to cancel in the sum
lean otter
If my divisor is 2x - 3, does the remainder theorem still work?
safe radishBOT
If my divisor is 2x - 3, does the remainder theorem still work?
flat frigateBOT
Jared
lean otter
My remainder would be 51, however, if I were to be asked for what values of x will make the P(x) = R(x) how would I do that?
According the remainder theorem I would assume 3, but that does not work
lean thorn
My remainder would be 51, however, if I were to be asked for what values of x wi...
the remainder for that division is 51/4, not 51
and according to the remainder theorem:
which checks out
lean thorn
$\left(\frac{3}{2}\right) + 5\left(\frac{3}{2}}\right) + 3 $
$\\ = \left(\frac{9}{4}}\right) + \left(\frac{30}{4}}\right) + \left(\frac{12}{4}}\right)$
$\\ = \left(\frac{51}{4}}\right)$
flat frigateBOT
MellowDramaLlama
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
lean thorn
Seems like I did my division wrong then
indeed it seems there might be a computation error
white crow
where did this come from?
safe radishBOT
where did this come from?
white crow
isnt gcd(10, 16) = 2?
worthy hemlock
It could have meant lcm(10, 16)
lean otter
how would one go about these questions? i am confused by their wording.
for example, would i be right to say that for 34(a) the answer would be ij?
I don't know how to even answer them
safe radishBOT
how would one go about these questions? i am confused by their wording.
for exam...
@lean otter Has your question been resolved?
lean otter
would the answer to 34(a) literally be
$\textbf{P+M+N}=[p_ij+m_ij+n_ij]$
flat frigateBOT
Verl
safe radishBOT
@lean otter Has your question been resolved?
drowsy moss
yes
lean otter
If i have 3 4 5 triangle
its angle should be
PI/2 radians
right?
gilded vault
If i have 3 4 5 triangle
its angle should be
PI/2 radians
right?
yeah the angle formed by the 3 and 4 side lengths yes
gilded vault
oh
lean otter
this is how im setting everything
constructor(x: number, y: number) {
this._x = x
this._y = y
this._angle = Math.atan2(y, x)
this._magnitude = Math.sqrt(x * x + y * y)```you are looking at the wrong angle is my guess
lean otter
you are looking at the wrong angle is my guess
Is atan2 the right function to use
gilded vault
Is atan2 the right function to use
yep your program is not calculating the right angle
your program is calculating the angle opposite the 3-side
so the angle formed by the 4 and the 5 side
gilded vault
why is it doing that lol
um because thats how arctan works if you give the opposite as 4 and the adjacent as 3
lean otter
um because thats how arctan works if you give the opposite as 4 and the adjacent...
so I did the wrong trig function?
Sorry I only know sine and cosine lol
Copilot auto suggested atan2
gilded vault
so I did the wrong trig function?
yes
lean otter
Wonder why copilot would get that wrong....
Maybe it's because the y axis in websites is upside down?
Would that make it the correct function?
If vertical space were flipped?
gilded vault
okay so here is the thing
you are given the legs of a right triangle in your program
you dont even need a trig funtion
the angle will always be 'right' in any vector the way you define it
lean otter
the angle will always be 'right' in any vector the way you define it
what if I make the x 7 and the y 20
that won't be a right angle
gilded vault
what if I make the x 7 and the y 20
well you are literally creating a right triangle with legs 7 and 20 with your program
lean otter
well you are literally creating a right triangle with legs 7 and 20 with your p...
How is that possible?
gilded vault
How is that possible?
um the 3rd side will equal sqrt(20^2+7^2)=sqrt(449)
okay so just make it clear about what you want your input to be and what you want your output to be
because that seems to be the big problem here
lean otter
so its a vector class
represented by X and Y
meant to embody an arrow in space
I dont know how to further articulate this lol
it's just a typical angle of a vector
It is not always going to be 90 degrees
The arrow might be facing 0 degree
lean otter
Oh I just confused which angle I was getting
The origin starts at the bottom left
that's what I want
static vale
Oh I just confused which angle I was getting
That red angle would be 53 degrees ig
Wait nvm I'm high idk what I am talking abt
gilded vault
yeah whatever your expect was wrong your program was the correct value
gilded vault
full value is 53.13010235
that would need to be converted into radians but yeah
lean otter
all good was that right?
Yes
gilded vault
we should probably use .close now
formal zodiac
want to know how to do it?
lean otter
.close
safe radishBOT
lean otter
want to know how to do it?
Do what. Get the number?
safe radishBOT
Available help channel!
granite cobalt
if the question asks you to draw a tree diagram and states the probability using percentage do you draw the tree using percentage or decimals
safe radishBOT
if the question asks you to draw a tree diagram and states the probability using...
granite cobalt
the question states to use appropiate probability
toxic stratus
i wouldnt think it would matter
safe radishBOT
@granite cobalt Has your question been resolved?
blazing valve
A student wants to determine the number of zeros for each of the given equations.
The equation x²+4x+3=0 has ? zeros.
The equation -x²+3x=0 has ? zeros
safe radishBOT
A student wants to determine the number of zeros for each of the given equations...
quasi bison
the quadratic formula,
quasi bison
and it is a little overkill here
though it's fine if you can't spot the factorization right away
blazing valve
@quasi bison @upbeat swan can u help me
blazing valve
help me step by step plz.
i missed some classes and my teacher isnt here for a week
so i cant get help
@upbeat swan
blazing valve
identify a,b and c
a = 1
b =4
c = 3
blazing valve
ive never learned the formula
upbeat swan
then can you factor the equation?
blazing valve
uhh no. i basically missed since day 1 of class
blazing valve
then can you factor the equation?
if u tell me what to do, then i might know
upbeat swan
factoring is harder than using the formula
blazing valve
factoring is harder than using the formula
teach me plz
blazing valve
@upbeat swan ok i factored it.
i got (x+3)(x+1)
upbeat swan
good
so we have (x+1)(x+3)=0
and we need to solve this
we have to think
a*b is 0
when
either a or b is 0
so we set each factor to be 0
(x+1)=0
(x+3)=0
solve these 2 equations and we're done
do you understand?
blazing valve
imma do it rn
upbeat swan
yes
upbeat swan
yes
blazing valve
ok but i have to find the number of zeros
upbeat swan
well how many zeros did you find
blazing valve
2?
upbeat swan
yes
blazing valve
how do i do -x^2+3x=0
safe radishBOT
@blazing valve Has your question been resolved?
safe radishBOT
@blazing valve Has your question been resolved?
safe radishBOT
@blazing valve Has your question been resolved?
cloud escarp
.reopen
lean otter
safe radishBOT
true crescent
Assuming cos x is not zero, just divide by cos ² x and see if you can finish it
lean otter
I'm left with 2=3sinx%cosx
true crescent
what is sinx/cosx
lean otter
Tan
true crescent
there you are
lean otter
?
true crescent
you want to find the value of tan, don't you
lean otter
Yh
lean otter
Thanks sir
true crescent
you're welcome
true crescent
sure
true crescent
cosec x =1/cos x so we get 1/cos x = 2
by multiplying and dividing we get ½=cos x
this should be easy now
lean otter
Isn't 1 on sin
true crescent
no, check your textbook
lean otter
lean otter
But my answer are not coming out like the one in the mcq
true crescent
½=sin x has the answer pi/6
lean otter
It's not there
true crescent
What other choices are there?
lean otter
5pi on 6
Pi on 3
Pi on 2
2pi on 3
lean otter
Sir 😅😅
lean otter
Yez
true crescent
what about sin(pi+x)=-sin(x)?
lean otter
Nope
true crescent
well then do you know sin(x+y)=sin(x)cos(y)+sin(y)cos(x)
lean otter
Yes
true crescent
then just plug in pi and -x
sin(pi-x)=sin(pi)cos(-x)+sin(-x)cos(pi)
=0+-sin(x)(-1)
=sin(x)
lean otter
sinx yh
lean otter
OK
true crescent
once you get this sin(5pi/6) because easy
for 5pi/6 = pi-pi/6
so sin(5pi/6)=sin(pi-pi/6)=sin(pi/6)
=½
using sin(pi-x)=sin(x)
true crescent
This is a bit more involved
you have to find cos theta using the identity sin²(theta)+cos²(theta)=1
Keeping in mind that cos theta is positive since theta is between 0 and pi/2
lean otter
Yh trig formula
true crescent
once you find that messy expression for cos theta, you can just expand sec theta + tan theta and simplify the mess
lean otter
😅