Question

In the figure below, the arc x is formed on the unit circle by angle θ . What is the measure of angle θ in radians? A x B π−x C π/2 D π

Answer 1

A. x radians

Explanation:

The circumference of the unit circle is

`2\pi r=2\pi \cdot 1=2\pi`

The full rotation angle has the measure
`2\pi` radians.

So,

`\begin{array}{cc}\text{Angle}&\text{Arc length}\\ \\2\pi &2\pi \\\theta &x\end{array}`

Write a proportion:

`(2\pi )/(\theta)=(2\pi )/(x)`

Cross multiply:

`2\pi x=2\pi \theta\\ \\\theta=x`