Question

unit circle trigonometry: foundations
which of the following radian measures is equal to 1,080°?
(the number of degrees of arc in a circle is 360. the number of radians of arc in a circle is 2π.)
choose 1 answer:
a 3π radians
b 6π radians
c 10π radians
d 12π radians
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Explanation:

Step1: Set up conversion ratio

We know that $360^{\circ}=2\pi$ radians. Let $x$ be the radian - measure for $1080^{\circ}$. Then $\frac{360^{\circ}}{2\pi}=\frac{1080^{\circ}}{x}$.

Step2: Cross - multiply and solve

$360x = 1080\times2\pi$. So $x=\frac{1080\times2\pi}{360}=6\pi$.

Answer:

B. 6π radians