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)
`(3\pi)/(2)` radians

Explanation:

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

Given: The arc length of a sector in the unit circle
`=(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=(3\pi)/(2)` in the above formula , we get

`(3\pi)/(2)=(1)x\\\\\Rightarrow\ x=(3\pi)/(2)`

Hence, the measure of the angle of the sector
`=(3\pi)/(2)` radians