Determine values of "a" that satisfy :

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[vale panther]

apex predator

[neat charm]

are you given a range or do they just want a value of alpha

[safe blaze]

just a value

[safe blaze]

confusing of the highest order

[vale panther]

apex predator

[safe blaze]

thats what i got originally

and it was wrong

[neat charm]

you have a second set of solutions too

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my teacher gave ONLY this as a note

thats all i have to decipher an alternative solution

[vale panther]

apex predator

[neat charm]

I assume you want positive values of alpha though

so you have that and 2π-π/80

+2nπ

[safe blaze]

It doesnt matter if its positive or no, as long as its the correct answer, they didnt give any specifications

[neat charm]

oh ok

[safe blaze]

the question they gave is as i have posted

[neat charm]

usually you want your constant term to be between 0 and 2π

with your 2nπ taking care of the rest

[safe blaze]

yeah

[neat charm]

so you have π-π/80 and 2π-π/80

both + 2nπ

[safe blaze]

so both of them are correct "or" solutions?

[neat charm]

both are solutions

[safe blaze]

I see

well ive asked like 20 people and they take the same approach

so its gotta be correct

[neat charm]

well it's a correct way of presenting it

[vale panther]

apex predator

[safe blaze]

so this is the correctomundo solution?

verygood

[neat charm]

well

that's some of the solutions

look up a graph of your function, you have a lot of other roots because your sines have different periods

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so can i write the solution like this?

[neat charm]

those are some of the values, yes

[safe blaze]

ik that 2pi*n goes infinitely out and gives an infinite solutions

but to present to my teacher

[neat charm]

you can get more solutions from those but with npi/2

[safe blaze]

is this sufficient to show the solutions?

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hmm

[neat charm]

have you done the trig addition formulae yet?

@safe blaze

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Is that necessary for this question?

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yes

i do math in swedish but i believe ik what u mean

[neat charm]

i reckon thats what your teachers want you to do

so you make your function = 0 right

[safe blaze]

OH, i did think about that yeah

go on

[vale panther]

apex predator

[neat charm]

then by the sine subtraction formula you can get

[vale panther]

apex predator

apex predator

[neat charm]

solve like a quadratic

[vale panther]

apex predator

[safe blaze]

wow

[neat charm]

gives you 4 pairs of viable solutions and you can adjust your period as necessary

for the individual ones

[neat charm]

as I said up here

you can see the period of your sine is 2alpha

so you can make your +2nπ now +nπ/2

and for the cos branch you can have +nπ/4

makes sense?

[neat charm]

my bad for not asking if you had done addition formulae yet

this problem is so much harder without using it

can you take it from here?

I actually really like this problem

[safe blaze]

hmm yeah i get it

[neat charm]

it's tricky, will (and probably has from what you told me) catch many people out

[safe blaze]

but

becayse its +2pin shouldnt cos branch be pin/2

and sin branch pi*n?

[safe blaze]

maybe...

[neat charm]

yeah that makes sense

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ill give it a shot

[neat charm]

my bad

I'm doing it without notes so thank you for correcting me

[safe blaze]

but yeah, very clever alternate solution

ill draw it out

[neat charm]

do you mind if I show this problem to my tutees?

or create a similar one

[safe blaze]

It's not trademarked so go ahead lol

[neat charm]

I know, but it's good practice to ask for the sake of academic honesty

[neat charm]

actually no i was correct

it is pi/4 and pi/2

because these functions are zeroing every half a period

you half and then divide by 2 or 4 or whatever

[safe blaze]

I see

Maan trig gets me all cooked up

[vale panther]

apex predator

[neat charm]

I can't say this often but I have to say that I don't think I've seen a problem like this in over 4 years

congratulations

[neat charm]

yeah i just checked and these are correct

so if you get those as your sols then good job

[safe blaze]

how did you get this from the image prior to it

theres a disconnect in my knowledge

[neat charm]

second from top

[safe blaze]

bro SAME. ive been telling him man. DONT BOTHER. LOSE THEE MARKS.

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AHH, i see

[neat charm]

i love this problem tbh

[safe blaze]

its not marks, if i dont solve it, im done for

toast

syrup

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yeah bcos ur a little nerd boy who's NOT better than me OBVIOUSLY. smh smh smh

[neat charm]

1 v 1 on STEP III

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i'd rather be hung than do trig problems foor a living

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cant be that bad

give us an "easy" problem

[neat charm]

theyre a little mid

this is the first problem

on a paper

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this shouldnt be too bad

whats step III?

[neat charm]

you have 20 minutes btw

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Kvasir, stay out of this my child.

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i will give myself 30 + tax

[neat charm]

allegedly one of the hardest undergraduate maths admissions exams in the world

[neat charm]

15

[neat charm]

i don't believe it

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admission exams? god have mercy

im gonna try that question

i will impress you

[neat charm]

ok, cya with your answer in 15 minutes

or under 10 minutes to beat my first time

[neat charm]

you solved it yet?

[safe blaze]

working on it my chum

im a slow mather

[neat charm]

no worries

[neat charm]

4 minutes

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ok

do i have to do all 3?

[neat charm]

yeah

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i managed to do the first one

:)

[neat charm]

2 minutes

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2nd one will be easy

[neat charm]

I'll be fairly impressed if you complete the whole thing under 20 tbf

[safe blaze]

man im really bad at math but ive been staring at cos(4a+9pi/40)=0 and sin(2a+pi/40)=0 for 15 min now and idk how to solve it. I simply dont have enough knowledge

like how do i proceed

[neat charm]

arccos(0)=pi/2

arcsin(0)=0

[safe blaze]

what???

i thought of that but it gives like a crazy decimal value on desmos

well

ig its radians

maaaaan

[neat charm]

2a+pi/40=0 and 4a+9pi/40=pi/2

[safe blaze]

im so fucking dumb

[neat charm]

nah

probably just tired of this problem

can't blame you

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lol nvm i give up

i only managed to do i)

[neat charm]

I'm still proud of you

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feel free to correct any mistakes/ ask about working, but im sure you know how to do this

idk where to go with ii), lowk a little to :D wacky for me

[safe blaze]

i got a = 11pi/160 + n*pi/4

[neat charm]

yeah great

[neat charm]

thats valid, see how that's pi/4 more than what i got

[safe blaze]

yeah

well

[neat charm]

integration by parts with a DI table can get the pattern fairly quickly

alternatively you apply the same sub as i and then use the cosine reduction formula

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so is that a correct solution for the cosine branch?

[neat charm]

yeah

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and -pi/80+pi*n/2

for sin

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bah that sucks, if i had paper i'd give it a try, otherwise, i guess i'll just tell myself i could have easily done it if i had tried, meanwhile here is my current working

cool

coolio boolio

[safe blaze]

BOOLEAN LOGIC?>??? ?REE REEEEEEEEEEE REEEEEE

[neat charm]

sec^2-2n is cos^2n sec^2 or cos^(2n-2)

[safe blaze]

makes sense

[neat charm]

you should also have cos^(2n-2)(1-sin^2)

[safe blaze]

@neat charm Ok i think thats all from me. I really appreciate your help sir 👍

[neat charm]

no problem

[safe blaze]

do you have more problems

:)

smt that i can do, but will also impress you

[neat charm]

no, i have to sleep soon

[safe blaze]

i mean me toto

[neat charm]

you've impressed me enough

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but

[neat charm]

this is dodgy though

[safe blaze]

shhh ;)

[neat charm]

alright bye, i'm gonna close this now

[safe blaze]

byaaaa

love you :)

[neat charm]

+close