Question

review the four points shown on the polar coordinate system. which point has coordinates (5, -\frac{7\pi}{6})? point a point b point c point d

Explanation:

Step1: Convert negative angle

\(-\frac{7\pi}{6}+2\pi=\frac{5\pi}{6}\)

Step2: Identify quadrant

\(\frac{5\pi}{6}\) is in second quadrant.

Step3: Select point

Point \(B\) is in second quadrant.

Answer:

We need to analyze the polar - coordinate \((r,\theta)=(5,-\frac{7\pi}{6})\). First, convert the negative angle to a positive equivalent. Add \(2\pi\) to \(-\frac{7\pi}{6}\), so \(-\frac{7\pi}{6}+2\pi = -\frac{7\pi}{6}+\frac{12\pi}{6}=\frac{5\pi}{6}\). In polar coordinates, \(r = 5\) is the distance from the origin and \(\theta=\frac{5\pi}{6}\) is the angle measured counter - clockwise from the positive \(x\) - axis. The angle \(\frac{5\pi}{6}\) is in the second quadrant. Among the points \(A\), \(B\), \(C\), and \(D\), point \(B\) is in the second quadrant. So the answer is point \(B\).