use the unit circle to find the exact value of the inverse trig function. remember the domain of inverse…

use the unit circle to find the exact value of the inverse trig function. remember the domain of inverse cosine is limited to quadrants i and ii (the top half of the unit circle).\n\n\\(\\cos^{-1}(-\\frac{1}{2})\\)\n\n a. 210°\n b. 30°\n c. 120°\n d. 360°

use the unit circle to find the exact value of the inverse trig function. remember the domain of inverse cosine is limited to quadrants i and ii (the top half of the unit circle).\n\n\\(\\cos^{-1}(-\\frac{1}{2})\\)\n\n a. 210°\n b. 30°\n c. 120°\n d. 360°

Answer

Explanation:

Step1: Recall unit - circle and inverse cosine domain

The domain of $y = \cos^{-1}(x)$ is $[- 1,1]$ and its range is $[0,\pi]$ (quadrants I and II). We need to find an angle $\theta$ in this range such that $\cos\theta=-\frac{1}{2}$.

Step2: Check cosine values on unit - circle

On the unit - circle, $\cos\theta$ is the $x$ - coordinate of the point on the unit - circle corresponding to the angle $\theta$. In quadrant II, when $\theta = 120^{\circ}$ (or $\frac{2\pi}{3}$ radians), $\cos\theta=-\frac{1}{2}$.

Answer:

C. $120^{\circ}$