Given Cos (2x)= -24/25, 2nd Quadrant (pi/2 <x< pi); What is Sin(x) ?

Question

Am I missing something big here? I've gotten around to making sin(2x)=7/25 but I don't understand how to go from double angle to single angle using identities.

Answer 1

Use one of the identities for cos(2x):

cos(2x) = cos²(x) – sin²(x)

OR:

1 – 2 sin²(x)

OR:

2 cos²(x) – 1

In this case, you want sin(x), so use: cos(2x) = 1 – 2 sin²(x)

2 sin²(x) = 1 - cos(2x)

sin(x) = √((1 - cos(2x) / 2)