Question

the angle $\frac{12\pi}{7}$ is in standard position. what quadrant is its terminal side in?
check
a. one
b. two
c. three
d. four

Explanation:

Step1: Determine the range of each quadrant in radians

• Quadrant I: \(0 < \theta<\frac{\pi}{2}\approx1.57\)
• Quadrant II: \(\frac{\pi}{2}<\theta<\pi\approx3.14\)
• Quadrant III: \(\pi<\theta<\frac{3\pi}{2}\approx4.71\)
• Quadrant IV: \(\frac{3\pi}{2}<\theta<2\pi\approx6.28\)

Step2: Compare \(\frac{12\pi}{7}\) with the range of each quadrant

Calculate \(\frac{12\pi}{7}\approx\frac{12\times3.14}{7}\approx5.34\)
Since \(4.71 < 5.34<6.28\) (i.e., \(\frac{3\pi}{2}<\frac{12\pi}{7}<2\pi\))

Answer:

d. Four