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
please select the best answer from the choices provided

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 $\theta_{rad}=-112\times\frac{\pi}{180}=-\frac{28\pi}{45}\approx - 1.95$ radians.

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 $\theta=-1.95$ radians, the distance traveled along the unit circle is approximately $1.95$ units, and the negative sign indicates the direction is clock - wise.

Answer:

D. 1.95 units clockwise