Question

for the given central angle, determine the distance traveled along the unit circle from the point (1, 0). 180° a. 1.57 units b. 3.14 units c. 3.14 units clockwise d. 1.57 units clockwise please select the best answer from the choices provided

Explanation:

Step1: Recall arc - length formula

The formula for the arc - length $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. For a unit circle, $r = 1$. First, convert the angle from degrees to radians. We know that to convert degrees to radians, we use the conversion factor $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$. Given $\theta_{deg}=180^{\circ}$, then $\theta_{rad}=\frac{\pi}{180}\times180=\pi\approx3.14$ radians.

Step2: Calculate arc - length

Since $r = 1$ and $\theta=\pi$ radians, using the formula $s = r\theta$, we get $s=1\times\pi\approx3.14$ units. The direction is not specified in the problem statement for the central - angle measurement in the context of the arc - length calculation from $(1,0)$. Usually, positive angles are measured counter - clockwise, but if we consider the general sense of the problem asking for the distance, we just focus on the magnitude of the arc - length.

Answer:

B. 3.14 units