Trigonometry question

Question

If csc ( x ) = 2 , for (90°< x < 180°), then

sin ( x/2)= ?

cos ( x/2 ) = ?

tan ( x 2 ) = ?

Answer 1

You can find the half-angle formulas here:

https://precalculusfinal.weebly.com/18-half-angle-identities.html

Note they have square-roots in them, so you need to be able to say if it’s the positive or negative answer. Note that if 90° ≤ x ≤ 180°, then 45° ≤ x/2 ≤ 90°. So the half-angle is in the first quadrant and all of sin, cos, tan are all positive.

Robert Clark

Answer 2

csc x = 2

sin x = 1/2

cos x = √3 / 2

Now substitute the values into the appropriate formula