Isaac Physics Maths Trig Solving Question

.Umar.

I'm stuck on part B of this question: https://isaacphysics.org/questions/fasttrack_stage1_q7_2018

tanx=4cosx
has two roots in the interval -180≤x≤180
These are denoted by α and β, where alpha < beta

Show alpha,α and beta,β on your sketch, and express beta,β in terms of alpha,α.

Im getting beta to be 118.02 degrees and alpha to be 61.98 degrees, but i cant get the answer that wants me to put Beta in terms of Alpha. I previously wrote beta = 61.98/118.02 alpha. Any help will be appreciated.

Reply 1

tande33

Original post by UmarSiddique

It doesn't actually want you to work out alpha and beta yet, use your knowledge on the sin (or other trig) functions to write a generalised answer I think. Get back to me if you are still stuck. :smile:

(I think you have the answer in some sense anyway)

Reply 2

qwert7890

Original post by UmarSiddique

I'm stuck on part B of this question: https://isaacphysics.org/questions/fasttrack_stage1_q7_2018

tanx=4cosx
has two roots in the interval -180≤x≤180
These are denoted by α and β, where alpha < beta

Show alpha,α and beta, on your sketch, and express beta,β in terms of alpha,α.

Im getting beta to be 118.02 degrees and alpha to be 61.98 degrees, but i cant get the answer that wants me to put Beta in terms of Alpha. I previously wrote beta = 61.98/118.02 alpha. Any help will be appreciated.

Your answers are correct, those are the values I am getting as well.

I know the problem - do you want to hear it? :biggrin:

If β= ~118, and α = 61.98, then to write β in terms of α, won't it be (118.02/61.98) times alpha as opposed to what you have done (61.98/118.02)

Basically you've done the complex math correctly, but have divided it the other way round. Happens to the best of us!

Reply 3

.Umar.

Original post by qwert7890

Your answers are correct, those are the values I am getting as well.

I know the problem - do you want to hear it? :biggrin:

I put it the other way round too but its not the correct answer apparently:

OnPaste.20201213-155254.jpg60.5KB

Reply 4

.Umar.

Original post by tande33

(I think you have the answer in some sense anyway)

im still very stuck xD. can i not just write beta in terms of alpha using degrees?

Reply 5

.Umar.

Original post by UmarSiddique

im still very stuck xD. can i not just write beta in terms of alpha using degrees?

would i write sine of alpha = (-1+sqrt(65))/8 and the sine of beta = (-1-sqrt(65))/8 ??

Reply 6

tande33

I am just going to give you the answer as its not clear what the question wants, its weird so brace yourself!
Answer:

Spoiler

Reply 7

qwert7890

Original post by tande33

I am just going to give you the answer as its not clear what the question wants, its weird so brace yourself!
Answer:

Spoiler

Oh!! I mean that is how you arrive to get beta (or alpha) anyway, but I thought you had to mention "how many times" is beta larger than alpha lmaooo

Reply 8

.Umar.

Original post by tande33

I am just going to give you the answer as its not clear what the question wants, its weird so brace yourself!
Answer:

Spoiler

aaah i see where i went wrong now. thanks for the help xD

Reply 9

tande33

Original post by qwert7890

Oh!! I mean that is how you arrive to get beta (or alpha) anyway, but I thought you had to mention "how many times" is beta larger than alpha lmaooo

Yeah its really odd, but if you look at part C there is no way that question would come after you have already worked out alpha and beta, that was the clue. Not great wording imo tho