Henry is asked to find the exact value of cosine StartFraction 10 pi Over 3 EndFraction. His steps are shown below. 1. Subtract
2 pi from StartFraction 10 pi Over 3 EndFraction as many times as possible: StartFraction 10 pi Over 3 EndFraction – 2 pi = StartFraction 4 pi Over 3 EndFraction 2. Find the reference angle for StartFraction 4 pi Over 3 EndFraction: StartFraction 3 pi Over 2 EndFraction – StartFraction 4 pi Over 3 EndFraction= StartFraction pi Over 6 EndFraction. 3. The cosine value for StartFraction pi Over 6 EndFraction is StartFraction StartRoot 3 EndRoot Over 2 EndFraction. 4. The cosine value is positive because StartFraction pi Over 6 EndFraction is in the first quadrant. Which of the following describes Henry’s errors? The reference angle should be StartFraction pi Over 3 EndFraction, and the sign of the value should be negative. The reference angle should be StartFraction pi Over 3 EndFraction, and the cosine value for StartFraction pi Over 3 EndFraction is One-half. The sign of the value should be negative, and the reference angle and quadrant should be determined by subtracting Pi in the first step. The cosine value for StartFraction pi Over 6 EndFraction is One-half, and the reference angle and quadrant should be determined by subtracting Pi in the first step.
