Question

for the given central angle, determine the distance traveled along the unit circle from the point (1, 0). -112° a. 0.98 units b. 0.62 units c. 0.62 units clockwise d. 1.95 units clockwise

Explanation:

Step1: Convert degrees to radians

The formula to convert degrees to radians is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg}=- 112^{\circ}$, then $\theta_{rad}=-112\times\frac{\pi}{180}=-\frac{28\pi}{45}$.

Step2: Recall arc - length formula on unit circle

The arc - length $s$ of a circle is given by $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. For a unit circle, $r = 1$. So, $s=\vert\theta\vert$. Since $\theta=-\frac{28\pi}{45}$, then $s=\vert-\frac{28\pi}{45}\vert\approx\vert-\frac{28\times3.14}{45}\vert=\vert-\frac{87.92}{45}\vert\approx1.95$. The negative sign of the angle indicates a clock - wise direction.

Answer:

d. 1.95 units clockwise