System of Measurement of Angles

Sexagesimal System

1 \text{ right angle } = 90^{\circ}

1^{\circ} = 60  \text{ minutes } = 60'

1' = 60 \text{ seconds } = 60''

Centesimal System

1 \text{ right angle } = 100  \text{ grads } = 100^g

1 \text{ grade } = 100  \text{ minutes } = 100'

1 \text{ minute } = 100  \text{ seconds }  = 100''

Circular System

Radian: One radian (1^c) , is the measure of the angle subtended at the center of a circle by an arc of length equal to the radius of the circle.

\displaystyle 1^c = \frac{angle}{\pi}

The number of radians in an angle subtended by an arc of a circle is equal to \frac{arc}{radius}

Relation between Degrees and Radians

\displaystyle 1^c = \frac{180^o}{\pi}