Chapter 6.2, Problem 117AYU

To determine

To find: The two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds to each angle is (12, 3v2).

Answer to Problem 117AYU

Solution:

  $\frac{\pi }{3},\frac{7\pi }{3},\frac{13\pi }{3}, -\frac{5\pi }{3},-\frac{11\pi }{3}$

Explanation of Solution

Given:

The point on the unit circle that corresponds to each angle is $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$ .

Calculation:

The point $\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$ corresponds to $\frac{\pi }{3}$

Therefore the positive angles lies in the points are $\frac{\pi }{3}$ , $\frac{\pi }{3}+2\pi$ , $\frac{\pi }{3}+4\pi$

i.e., $\left(\frac{\pi }{3},\frac{7\pi }{3},\frac{13\pi }{3}\right)$

Therefore the negative angles lies in the points are $\frac{\pi }{3}-2\pi ,\frac{\pi }{3}-4\pi$

i.e., $\left(-\frac{5\pi }{3},-\frac{11\pi }{3}\right)$