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Multiple Choice
For each expression, identify which coterminal angle to use & determine the exact value of the expression. sin37π
A
21
B
2
C
23
D
323
Verified step by step guidance
1
Identify the given angle: \( \frac{7\pi}{3} \). This angle is in radians.
Find a coterminal angle between \( 0 \) and \( 2\pi \) by subtracting \( 2\pi \) from \( \frac{7\pi}{3} \) until the angle is within the desired range.
Calculate \( \frac{7\pi}{3} - 2\pi \). Convert \( 2\pi \) to a fraction with a denominator of 3: \( \frac{6\pi}{3} \).
Subtract the fractions: \( \frac{7\pi}{3} - \frac{6\pi}{3} = \frac{\pi}{3} \). This is the coterminal angle.
Determine the exact value of \( \sin\left(\frac{\pi}{3}\right) \). The sine of \( \frac{\pi}{3} \) is \( \frac{\sqrt{3}}{2} \).