Find the exact value of sin ?/2 , given that tan ? = 8/15 and p<?<3p/2

Question

This is for a test review please do it step by step 

Answer 1

draw a right triangle

tan=opposite/adjacent

tan=8/15

find the hypotenuse

c²=8²+15²

c²=64+225

c²=289

c=17

sin=opposite/hypotenuse

sin=8/17

Now look at Harvey F.'s solution. I read the problem as (sinx)/2 by mistake instead of sin(x/2).

 

 

 

Answer 2

Hi Ethan,

Using tan x = 8/15 = opp./adj. in a right triangle with acute angle x.

The hypotenuse is then 17 using the Pythagorean theorem.

so sin x = 8/17 and cos x = 15/17.

The half-angle equation for sin (x/2) = √(1/2)(1-cos x)

sin (x/2) = √(1/2)[1-(15/17)]