### RADIANS AND DEGREES

Radians and Degrees are two units of measurement used to express angles.

The radian is denoted by the symbol rad and it is the system of units (SI) for angles.

The angle subtended when traveling a distance equal to the radius around a circle is known as the radian. The subtended angle after one complete rotation is equal to 2\pi radians.

The degree is denoted by (^{\circ}). A full circle divided into 360 is called degrees. Each degree can be further divided in minutes(‘) and seconds(”).

1^{\circ}

1’=60”

We can use the protractor to measure the angle

#### RADIANS TO DEGREE

2\pi radians = 360 Degrees

\pi radians = 180 Degrees

**Equation**

degrees = radians x \left(\frac{180}{\pi}\right)

Example: Convert \left(\frac{\pi}{3}\right) to radians

Degrees = \left(\frac{\pi}{3}\right)\times\left(\frac{180}{\pi}\right)

= \frac{180\pi}{3\pi}

= 60^{\circ}

Some common radians value in degrees

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

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

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

\frac{2\pi}{3} = 120^{\circ}

\frac{3\pi}{4} = 135^{\circ}

\frac{5\pi}{6} = 150^{\circ}

{\pi} = 180^{\circ}

\frac{3\pi}{2} = 270^{\circ}

{2\pi} = 360^{\circ}

#### DEGREE TO RADIANS

360 Degrees = 2\pi radians

180 Degrees = \pi radians

**Equation**

radians = degrees x \left(\frac{\pi}{180}\right)

Example: Convert 30^{\circ} to radians

Degrees = 30\times\left(\frac{\pi}{180}\right)

= \frac{30\pi}{180}

Reduced by 30

= \frac{\pi}{6}

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