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: Understand polar coordinates

In polar coordinates $(r,\theta)$, $r = 5$ is the distance from the origin and $\theta=-\frac{7\pi}{6}$. A negative angle means rotation clock - wise.

Step2: Convert negative angle to positive equivalent

$-\frac{7\pi}{6}+2\pi=\frac{- 7\pi + 12\pi}{6}=\frac{5\pi}{6}$.

Step3: Locate the point

For $r = 5$ and $\theta=\frac{5\pi}{6}$ (or original $-\frac{7\pi}{6}$), we start from the positive x - axis, rotate clock - wise (or counter - clockwise for equivalent positive angle) and move out a distance of 5 units. This locates us at point D.

Answer:

point D