Question

How do you use the double angle or half angle formulas to find the exact value of cos2x, when `sinx=(sqrt 5)/3` and `pi/2 <= x <= pi`?

Answer 1

Find cos 2x knowing `sin x = sqrt5/3`

Ans: cos 2x = -0.11

Explanation:

Apply the trig identity: `cos 2x = 1 - 2sin^2 x`. We get:

`cos 2x = 1 - 2(5/9) = (9 - 10)/9 = -1/9 = - 0.11`

Check by calculator.
`sin x = sqrt5/3 = 2.24/3 = 0.745` --> arc `x = 48^@16` -->
--> `2x = 96^@32` --> `cos 2x = - 0.11 = -1/9`. OK