Question

If the arc length of a sector in the unit circle is 3π/2 , what is the measure of the angle of the sector? A) 0 radians B) π/2 radians C) π radians D) 3π/2 radians

Answer 1

D the answer is already in radians

Answer 2

Answer: D) $\dfrac{3\pi}{2}$ radians

Step-by-step explanation:

In geometry, the radius of a unit circle = 1 unit.

Given: The arc length of a sector in the unit circle $=\dfrac{3\pi}{2}$

We know that the formula to calculate length of arc having central angle x and radius r is given by  :-

$l=rx$

Substitute r= 1  and  $l=\dfrac{3\pi}{2}$ in the above formula , we get

$\dfrac{3\pi}{2}=(1)x\\\\\Rightarrow\ x=\dfrac{3\pi}{2}$

Hence, the  measure of the angle of the sector $=\dfrac{3\pi}{2}$ radians