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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