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\\(\\cos^{-1}(-1)\\)\n\\(\\text{a. }180^{circ}\\)\n\\(\\text{b. }90^{circ}\\)\n\\(\\text{c. }270^{circ}\\)\n\\(\\text{d. }0^{circ}\\)

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\\(\\cos^{-1}(-1)\\)\n\\(\\text{a. }180^{circ}\\)\n\\(\\text{b. }90^{circ}\\)\n\\(\\text{c. }270^{circ}\\)\n\\(\\text{d. }0^{circ}\\)

Answer

Explanation:

Step1: Recall cosine on unit - circle

The cosine of an angle $\theta$ in the unit - circle is the $x$ - coordinate of the point on the unit - circle corresponding to the angle $\theta$.

Step2: Find angle with $\cos\theta=-1$

We know that on the unit - circle, for $\theta = 180^{\circ}$ (or $\pi$ radians), the point is $(-1,0)$. So, $\cos(180^{\circ})=-1$. Also, since the domain of $y = \cos^{-1}(x)$ is limited to quadrants I and II (where $y\geq0$ in terms of the $y$ - coordinate on the unit - circle), and $\cos(180^{\circ})=-1$, then $\cos^{-1}(-1)=180^{\circ}$.

Answer:

A. $180^{\circ}$