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Coterminal Angles

In these lessons, we will look at angles at standard position and coterminal angles.

Related Topics:
More Lessons on Trigonometry

An angle is said to be in standard position if it is drawn on the Cartesian plane (x-y plane) on the positive x-axis and turning counter-clockwise (anti-clockwise).

The initial side of an angle is the ray where the measurement of an angle starts.

The terminal side of an angle is the ray where the measurement of an angle ends.

Co-terminal angles are angles which when drawn at standard position share a terminal side. For example, 30°, -330°, 390° are all coterminal.

We can find the coterminal angles of a given angle by using the following formula:

Coterminal angles of a given angle θ may be obtained by either adding or subtracting a multiple of 360° or 2π radians. 

Coterminal of θ = θ + 360° × k  if θ is given in degrees,
Coterminal of θ = θ + 2π ×k if θ is given in radians.

Two angles are coterminal if the difference between them is a multiple of 360° or 2π.


Determine if the following pairs of angles are coterminal

a) 10°, 370°
b) –520°, 200°
c) –600°, –60°


a) 10° – 370° = –360° = –1(360°), which is a multiple of 360°
So, 10° and 370° are coterminal

b) –520° – 200° = –720° = –2(360°), which is a multiple of 360°
So, –520 and 200° are coterminal

c) –600° – (–60°) = –540°, which is not a multiple of 360°
So, –600° and –60° are not coterminal


Coterminal Angles - Example 1.
This video discusses what it means for two angles to be coterminal, and discuss a quick method on how to decide if two angles are in fact coterminal. It also shows a couple of examples of finding angles that are coterminal to each other.
Coterminal Angles - Example 2.
More questions about deciding if angles are coterminal or not.

Basic Cartesian Coordinate System, Angles in Standard Position, Coterminal Angles
Coterminal Angles, Complementary Angles, Supplementary Angles in Radians

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