Degrees and Radians
Measurement of Angles
On a Cartesian coordinate system, we draw a circle centred at the origin and with radius 1.
Let P be a point on the circle.
The line OP and the positive x-axis form an angle
Let us agree that an angle measured counter-clockwise is positive, and an angle measured clockwise is negative. (See diagram below.)
Starting from the positive x-axis, the point P travels around the circle in a counter-clockwise manner.
If the point travels clockwise, when it hits the negative y-axis its angle will measure -90° and when it hits the negative x-axis its angle will measure -180°.
If the length of the arc from (1, 0) to P is 1unit we say the angle is 1 radian ( rad in short). When the unit of an angle is absent, we assume it is in radians.
The circumference of the circle of radius 1 is 2π or 2π radians.
So, measuring counter-clockwise,
2π = 360° and π = 180°.
This provides us with the following conversion formulas for changing between degrees D and radians R: