A central angle of a circle measures 315^\circ. What is the radian measure of this angle? — ACT

A central angle of a circle measures $315^\circ$ . What is the radian measure of this angle?

\frac{7\pi}{4}

To convert degrees to radians, multiply the degree measure by

\frac{\pi}{180^\circ}

. Multiplying

315^\circ

\frac{\pi}{180^\circ}

gives

\frac{315\pi}{180}

. Simplifying the fraction by dividing the numerator and the denominator by their greatest common divisor, 45, results in

\frac{7\pi}{4}

radians.

Set up the conversion from degrees to radians.

Multiply

315^\circ

by the conversion factor

\frac{\pi}{180^\circ}

The conversion factor from degrees to radians is

\frac{\pi}{180^\circ}

because a straight angle of

180^\circ

is equivalent to

\pi

radians.

Perform the multiplication and simplify the resulting fraction.

315 \times \frac{\pi}{180} = \frac{315\pi}{180} = \frac{7\pi}{4}

Dividing both the numerator 315 and the denominator 180 by their greatest common divisor, 45, yields the simplified fraction

\frac{7}{4}

To convert an angle from degrees to radians, multiply the degree measure by

\frac{\pi}{180^\circ}

and simplify the resulting fraction.

Estimated Time:45s

Question