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
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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]