Match each angle measure in degrees on the left to its equivalent angle measure in radians… — ACT

Match each angle measure in degrees on the left to its equivalent angle measure in radians on the right.

The degree measures

30^\circ

45^\circ

60^\circ

, and

90^\circ

correspond to

\frac{\pi}{6}

\frac{\pi}{4}

\frac{\pi}{3}

, and

\frac{\pi}{2}

radians, respectively.

Each degree measure matches its correct radian value by multiplying the degree measure by

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

and simplifying the fraction.

Apply the degree-to-radian conversion formula.

Multiply each degree measure by the conversion factor

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

A full circle has

360^\circ

2\pi

radians, meaning

180^\circ = \pi

radians. Therefore, the conversion factor from degrees to radians is

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

Simplify the resulting fractions.

30^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{6}

45^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{4}

60^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{3}

, and

90^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{2}

Reducing the fractions by dividing the numerator and denominator by their greatest common factor gives the simplified radian values.

Converting degree measures to radian measures on the unit circle

Estimated Time:45s

Question