use the circle shown in the rectangular coordinate system to find two angles, in radians, between - 2π and…

Explanation:

Step1: Recall angle - terminal side concept

Angles in standard position have terminal sides passing through the origin. Coterminal angles have the same terminal side.

Step2: Consider general form of coterminal angles

If $\theta$ is an angle, then coterminal angles are given by $\theta + 2k\pi$, where $k\in\mathbb{Z}$. We want angles in the interval $(- 2\pi,2\pi)$. Let's assume the reference - angle for the indicated point is $\alpha$. Without seeing the specific point, if the reference - angle is $\alpha$, one angle $\theta_1=\alpha$ and another angle $\theta_2=\alpha - 2\pi$ (if $\alpha>0$) or $\theta_2=\alpha + 2\pi$ (if $\alpha<0$) such that both are in the interval $(-2\pi,2\pi)$.

For example, if the point is on the positive $x$ - axis, the angles are $0,- 2\pi$ (but $-2\pi$ is not in the open interval $(-2\pi,2\pi)$, so the angles are $0$ and $0 - 2\pi+2\pi = 0$). If the point is on the positive $y$ - axis, the angles are $\frac{\pi}{2},\frac{\pi}{2}-2\pi=-\frac{3\pi}{2}$.

Let's assume the indicated point corresponds to an angle $\theta$ measured counter - clockwise from the positive $x$ - axis. If $\theta$ is the principal angle (the angle in $[0,2\pi)$), and $\theta\in(0,2\pi)$, then one angle is $\theta$ and the other is $\theta - 2\pi$. If $\theta\in(-2\pi,0)$, then one angle is $\theta$ and the other is $\theta + 2\pi$.

Answer:

Without seeing the specific point on the circle, we cannot give a numerical answer. But in general, if the principal angle (angle in $[0,2\pi)$) corresponding to the point is $\theta$, the two angles are $\theta,\theta - 2\pi$ (if $\theta>0$) or $\theta,\theta + 2\pi$ (if $\theta<0$) provided they are in the interval $(-2\pi,2\pi)$.