Angle

Angle

An angle is defined as the amount of rotation between two rays. Angles are measured using degrees and radians. A full rotation in degrees is 360°. A full rotation in radians is approximately 6.283 radians or τ (tau) radians.

Degrees

Degrees are a unit that measure angles. A full rotation in degrees is equal to 360°. By convention, an angle by itself is drawn with the first ray in the positive right direction. The counter-clockwise direction is the positive direction.

Radians

Similar to degrees, radians are a unit that measure angles using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.

Types of Angles

Acute Angle Notation
Acute Angle

An acute angle is an angle that is smaller than 90 degrees or PI fourths.

Obtuse Angle Notation
Obtuse Angle

An obtuse angle is an angle that is larger than 90 degrees or PI fourths.

Perpendicular Angle Notation
Perpendicular Angle

A Perpendicular angle, sometimes also referred to as a square angle, is exactly 90 degrees or PI fourths.

Complementary Angles | Notation

Complementary angles can visually be denoted as two angles who sum to a perpendicular or square angle.

Supplementary Angles | Notation

Supplementary angles can visually be denoted as two angles who sum to 180 degrees or PI degrees.

Usage

Polar Coordinate System | Concept

The Polar Coordinate System describes points in space using an angle and radius relative to the origin.

Right Triangle | Concept

A right triangle is a triangle where one of the three angles is a perpendicular angle. There are three sides of the right triangle: the adjacent, opposite, and hypotenuse sides.

Trigonometric Functions | Concept

There are six total trigonometric functions that relate to the geometry of the right-triangle sine, cosine, tangent, cosecant, secant, and cotangent. The functions take the angle of a right triangle as input and return a ratio of two of its sides.