Question

For each angle θ listed below, find the reference angle α, and then find sin θ. Round sin θ to four decimal places, if necessary.θ = 255° ? ?

Answer 1

The answer is option C. sin75=0.9659 sin255=-0.9659

Explanation:

Answer 2

A reference angle is the angle created by the terminal arm and X-axis, and must be in the same quadrant as the terminal arm.

The given angle is 255°. It is located at quadrant III, then we can find the reference angle by subtracting 180°:

`255\degree-180\degree=75\degree`

The sin of 75 is:

`\sin 75\degree=0.9659`

In quadrant III, the sine is negative, then the sin of 255° is equal to the sine of 75° but negative. So:

`\sin 255\degree=-0.9659`

The answer is option C. sin75=0.9659 sin255=-0.9659