Radians Math Example 3

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Example 3

medium
Convert 7π4\frac{7\pi}{4} radians to degrees and identify which quadrant this angle is in.

Solution

  1. 1
    7π4×180°π=7×180°4=315°\frac{7\pi}{4} \times \frac{180°}{\pi} = \frac{7 \times 180°}{4} = 315°.
  2. 2
    315°315° is between 270°270° and 360°360°, so it is in Quadrant IV.

Answer

315°, Quadrant IV315°, \text{ Quadrant IV}
To convert radians to degrees, multiply by 180°π\frac{180°}{\pi}. Quadrant identification: QI (0°0°-90°90°), QII (90°90°-180°180°), QIII (180°180°-270°270°), QIV (270°270°-360°360°). The angle 7π4\frac{7\pi}{4} is π4\frac{\pi}{4} short of a full revolution.

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 1 easy

Convert [formula] to radians.

Example 2 medium

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

Example 4 hard

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

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