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

Answer:

A. x radians

Step-by-step 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:

$\dfrac{2\pi }{\theta}=\dfrac{2\pi }{x}$

Cross multiply:

$2\pi x=2\pi \theta\\ \\\theta=x$