Double-Angle and Half Angle Identities. Double-Angle Identity. If represents the measure of an angle, then the following identities hold for all values of . If and terminates in the first quadrant, find the exact value of each function. -1.
Since 15⁰ is a first quadrant angle and sine is positive in the first quadrant, choose the positive value.
Since 135 is a second quadrant angle and cosine is negative in the second quadrant, choose the negative value. Thus,