Question

for the given central angle, determine the distance traveled along the unit circle from the point (1, 0). 218° a. 1.21 units clockwise b. 3.80 units c. 7.61 units d. 1.90 units please select the best answer from the choices provided

Explanation:

Step1: Convert degrees to radians

We know that to convert degrees to radians, we use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 218^{\circ}$, then $\theta_{rad}=218\times\frac{\pi}{180}=\frac{109\pi}{90}\approx 3.80$ radians.

Step2: Recall arc - length formula

The arc - length $s$ of a circle with radius $r$ and central angle $\theta$ (in radians) is given by $s = r\theta$. For a unit circle, $r = 1$. So, $s=\theta$. Since $\theta\approx3.80$ radians, the distance traveled along the unit circle from the point $(1,0)$ is approximately 3.80 units.

Answer:

B. 3.80 units