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

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 πx C π2 D π class=

Respuesta :

frika

Answer:

A. x radians

Step-by-step explanation:

The circumference of the unit circle is

[tex]2\pi r=2\pi \cdot 1=2\pi[/tex]

The full rotation angle has the measure [tex]2\pi[/tex] radians.

So,

[tex]\begin{array}{cc}\text{Angle}&\text{Arc length}\\ \\2\pi &2\pi \\\theta &x\end{array}[/tex]

Write a proportion:

[tex]\dfrac{2\pi }{\theta}=\dfrac{2\pi }{x}[/tex]

Cross multiply:

[tex]2\pi x=2\pi \theta\\ \\\theta=x[/tex]