if the arc length of a sector in the unit circle is $\frac{3pi}{2}$, what is the measure of the angle of the…

if the arc length of a sector in the unit circle is $\frac{3pi}{2}$, what is the measure of the angle of the sector?\na 0 radians\nb $\frac{pi}{2}$ radians\nc $pi$ radians\nd $\frac{3pi}{2}$ radians

if the arc length of a sector in the unit circle is $\frac{3pi}{2}$, what is the measure of the angle of the sector?\na 0 radians\nb $\frac{pi}{2}$ radians\nc $pi$ radians\nd $\frac{3pi}{2}$ radians

Answer

Explanation:

Step1: Recall the arc - length formula

The arc - length formula for a circle is (s = r\theta), where (s) is the arc length, (r) is the radius of the circle, and (\theta) is the central angle in radians.

Step2: Substitute the values for the unit circle

For a unit circle, (r = 1). Given (s=\frac{3\pi}{2}), substituting into (s = r\theta) gives (\frac{3\pi}{2}=1\times\theta).

Answer:

D. (\frac{3\pi}{2}) radians