Given that sin(2x) = 24/25, and 45 degrees < x < 90 degrees, find cos(2x)

Answer 1

Since 45º < x < 90º, 90º < 2x < 180º.

So, cos(2x) < 0

sin²(2x) + cos²(2x) = 1. So, cos²(2x) = 1 - sin²(2x).

Therefore, cos(2x) = ±√{1 - sin²(2x)) = ±√ (1 - (24/25)²) = ±√(49/25)² = ±7/25

But, since cos(2x) < 0, we have cos(2x) = -7/25.

Answer 2

This problem is just throwing you a curve ball, which is that 2x is NOT in quadrant 1 but in quadrant 2.

If you just consider a right triangle in which the sine of one angle is 24/25, the other leg is 7 and the cos of the angle specified is 7/25. . Since sin(2x) is positive in quadrants 1 and 2; the angle you need is about 106°

since 1/2 of this angle must be between 45 and 90.

The cos of this angle is -7/25.

The nuisance in this question is to determine the sign of the answer.