Question

SOMEONE PLEASE HELP! I'VE BEEN STUCK FOR AN HOUR!!!

Find the exact values of sin(x/2) and cos 2x given tan x= 8/15 and 180 12 years ago

Answer 1

Do you know the half-angle and double angle formulas to rewrite sin(x/2) and cos(2x) in terms of sin(x) and cos(x) ?

Answer 2

I know the formulas. I just don't know how I'm supposed to re-write it.

Answer 3

From \( \tan x = \dfrac{8}{15} \), I believe you can set up a right triangle and determine \( \sin x \) and \(\cos x \). The specification on angles for x means tan x is positive but both sin and cos are negative values. But with both sin x and cos x known, you could substitute their values in for whatever sin(x/2) and cos(2x) break into by the formulas.

Answer 4

I tried that and got an answer of 3 square root 34 over 34
The back of the book says that's not the answer

Answer 5

@AccessDenied

Answer 6

What is the back of the book's answer? And perhaps seeing your process would help spot an issue too.

Answer 7

The back of the book says the answer is 4 square roots of 17 over 17 for the sin

and 161/289 for the cos

Answer 8

@AccessDenied

Answer 9

Those files don't seem to work for me / are not supported on this computer...
If it is possible to add a different format or post it here, that'd be helpful. I am going to work this one out for myself as well.

Answer 10

I'm not sure how to change the file type. I took the picture on my phone, sent it to my email, and opened the email on my computer, saved the picture, and uploaded it here. When I saved it to my computer, it didn't give me an option to change the file type.

Answer 11

@AccessDenied

Answer 12

Someone please help this person.

Answer 13

I am assuming you obtained the hypotenuse of 17 to get those answers.
h = sqrt(15^2 + 8^2) = sqrt(289) = 17
So that
sin x = 8/17, cos x = 15/17
That is clear so far?

Answer 14

Find the exact values of sin(x/2) and cos 2x given tan x= 8/15 and 180<x<3(180)/2