Angles in Standard Position and Radian Measures

An angle in standard position is an angle whose vertex is at the origin of a coordinate system and whose initial side lies along the positive x-axis.

To find a coterminal angle, add or subtract multiples of 360° (or 2π radians) to the given angle.

Degrees and radians are two units for measuring angles. 180° is equivalent to π radians.

A positive coterminal angle for -90° is 270° (since -90° + 360° = 270°).

A negative coterminal angle for 150° is -210° (since 150° - 360° = -210°).

To convert degrees to radians, multiply the degree measure by $$\frac{\text{π}}{180}$$ .

To convert radians to degrees, multiply the radian measure by $$\frac{180}{\text{π}}$$ .

The standard position of an angle is when its vertex is at the origin and its initial side is along the positive x-axis.

The coterminal angles of -225° are 135° and -585°.

The degree measure of a full rotation is 360°.