Radians Math Example 1

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Example 1

easy
Convert 150°150° to radians.

Solution

  1. 1
    Use the conversion factor: 180°=π180° = \pi radians.
  2. 2
    Multiply: 150°×π180°=150π180150° \times \frac{\pi}{180°} = \frac{150\pi}{180}.
  3. 3
    Simplify: 150π180=5π6\frac{150\pi}{180} = \frac{5\pi}{6}.

Answer

5π6 radians\frac{5\pi}{6} \text{ radians}
Radians measure angles by the arc length subtended on a unit circle. Since the full circle has circumference 2π2\pi, a full rotation is 2π2\pi radians =360°= 360°. The conversion factor π180\frac{\pi}{180} converts degrees to radians.

About Radians

A radian is an angle measurement defined by the arc length it subtends on a unit circle: one radian is the angle at which the arc length equals the radius. A full circle is 2π2\pi radians (about 6.28 radians), making radians the natural unit for trigonometry and calculus.

Learn more about Radians →

More Radians Examples

Example 2 medium

Find the arc length of a sector with radius [formula] cm and central angle [formula] radians.

Example 3 medium

Convert [formula] radians to degrees and identify which quadrant this angle is in.

Example 4 hard

A wheel of radius [formula] cm rotates at [formula] rpm (revolutions per minute). Find the angular v

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