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 2π2\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

2π2\pi radians = 360 Degrees

π\pi radians = 180 Degrees

Equation

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

Example: Convert (π3) \left(\frac{\pi}{3}\right) to radians

Degrees = (π3)×(180π)\left(\frac{\pi}{3}\right)\times\left(\frac{180}{\pi}\right)

               = 180π3π\frac{180\pi}{3\pi}

               = 60^{\circ}

Some common radians value in degrees

π6\frac{\pi}{6} = 30^{\circ}

π4\frac{\pi}{4} = 45^{\circ}

π2\frac{\pi}{2} = 90^{\circ}

2π3\frac{2\pi}{3} = 120^{\circ}

3π4\frac{3\pi}{4} = 135^{\circ}

5π6\frac{5\pi}{6} = 150^{\circ}

π{\pi} = 180^{\circ}

3π2\frac{3\pi}{2} = 270^{\circ}

2π{2\pi} = 360^{\circ}

DEGREE TO RADIANS

360 Degrees = 2π2\pi radians 

180 Degrees = π\pi radians 

Equation

radians = degrees x (π180)\left(\frac{\pi}{180}\right)

Example: Convert 30^{\circ} to radians 

Degrees = 30×(π180)30\times\left(\frac{\pi}{180}\right)

               = 30π180 \frac{30\pi}{180}

                  Reduced by 30

               = π6 \frac{\pi}{6}

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