Definition

An angle (Θ) is composed of: an initial side (AB), a terminal side (BC), and a vertex (B).

Radian

Relates the size of a circle with the opening of an angle. One radian is the angle portrayed by the distance of the radius travelled along the circumference.

Radian Measurement

Any length (s) travelled along the circumference of a circle can be translated to an angle (Θ) rotated within it.

Degree

Method of measuring an angle which splits a full rotation up into 360 degrees, then describes the gap as a quantity of these degrees.

Pi

A constant which relates the diameter (d) of a circle to its circumference (C).

Degrees to Radians

Multiply the amount of degrees by pi and divide by 180 to convert the angle to radians.

Radians to Degrees

Multiply the amount of radians by 180 and divide by pi to convert the angle to degrees.

Coterminal Angles

Coterminal angles share the same sides and vertexes, but differ in their number of rotations.

Coterminal Formulas

Two angles are coterminal if they equal each other plus or minus an integer (k) multiplied by 360° (or 2π radians).

Acute Angle

Any angle between 0° and 90°.

0°<Θ<90°

Right Angle

An angle equals to 90°.

Θ=90°

Obtuse Angle

Any angle between 90° and 180°.

90°<Θ<180°

Straight Angle

An angle equals to 180°.

Θ=180°

Positive Angle

An angle measured counter-clockwise (Θ).

Negative Angle

An angle measured clockwise (-Θ).