Question

for the given central angle, determine the distance traveled along the unit circle from the point (1, 0).
57°
a. 0.99 units
c. 57 units
b. 1.99 units
d. 0.50 units
please select the best answer from the choices provided
o a
o b
o c
o d

Explanation:

Step1: Convert degrees to radians

The formula to convert degrees to radians is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 57^{\circ}$, then $\theta_{rad}=57\times\frac{\pi}{180}=\frac{57\pi}{180}\approx 0.99$ radians.

Step2: Recall arc - length formula for unit circle

For a unit circle ($r = 1$), the arc - length formula is $s=r\theta$, where $s$ is the arc - length (distance traveled along the circle), $r$ is the radius of the circle, and $\theta$ is the central angle in radians. Since $r = 1$ and $\theta\approx0.99$ radians, $s\approx0.99$ units.

Answer:

A. 0.99 units