Find cos2x

Question

Given that sin x=-3/5 and angle x lies in quad 3

Answer 1

Use the double angle formula:  cos2x = 1 - 2sin²x.

 

Therefore, if sinx = -3/5, and sin²x = 9/25,

 

cos2x = 1 - 2(9/25) = 1 - 18/25 = 25/25 - 18/25 = 7/25.

 

BUT: Since the angle lies in quadrant 3, (π < x < 3π/2), the double angle, 2x lies between 2π and 3π, and therefore could be ±7/25.