Identify the reference angle of each given angle. 47π rad
A
6π
B
4π
C
3π
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검증된 단계별 안내
1
Step 1: Understand the concept of a reference angle. A reference angle is the smallest angle that the terminal side of a given angle makes with the x-axis. It is always positive and less than or equal to π/2 radians.
Step 2: For the angle \( \frac{7\pi}{4} \), determine its position on the unit circle. Since \( \frac{7\pi}{4} \) is greater than \( \pi \), it is in the fourth quadrant. To find the reference angle, subtract \( \frac{7\pi}{4} \) from \( 2\pi \).
Step 3: For the angle \( \frac{\pi}{6} \), determine its position on the unit circle. Since \( \frac{\pi}{6} \) is less than \( \pi \), it is in the first quadrant. The reference angle is the angle itself, \( \frac{\pi}{6} \).
Step 4: For the angle \( \frac{\pi}{3} \), determine its position on the unit circle. Since \( \frac{\pi}{3} \) is less than \( \pi \), it is in the first quadrant. The reference angle is the angle itself, \( \frac{\pi}{3} \).
Step 5: Compare the reference angles found: \( \frac{\pi}{4} \) is the reference angle for \( \frac{7\pi}{4} \), \( \frac{\pi}{6} \) for \( \frac{\pi}{6} \), and \( \frac{\pi}{3} \) for \( \frac{\pi}{3} \). The correct answer is \( \frac{\pi}{4} \) as the reference angle for \( \frac{7\pi}{4} \).