Radian Measure Math Example 3

Follow the full solution, then compare it with the other examples linked below.

easy

Convert: (a)

60°

to radians, (b)

270°

to radians, (c)

\dfrac{\pi}{3}

to degrees, (d)

\dfrac{7\pi}{6}

to degrees.

1
(a) $60 \times \frac{\pi}{180} = \frac{\pi}{3}$ rad. (b) $270 \times \frac{\pi}{180} = \frac{3\pi}{2}$ rad.
2
(c) $\frac{\pi}{3} \times \frac{180}{\pi} = 60°$ . (d) $\frac{7\pi}{6} \times \frac{180}{\pi} = \frac{7\times180}{6} = 210°$ .

Answer

(a)

\frac{\pi}{3}

, (b)

\frac{3\pi}{2}

, (c)

60°

, (d)

210°

The conversion formula is straightforward: degrees

\times \pi/180 =

radians; radians

\times 180/\pi =

degrees. Memorizing common conversions (

30°=\pi/6

45°=\pi/4

60°=\pi/3

90°=\pi/2

) speeds up work.

About Radian Measure

An angle measure defined by the arc length subtended on a unit circle: one radian is the angle that subtends an arc equal in length to the radius.

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