Mathematical Calculators

Coterminal Angle Calculator

Find out coterminal angles with our coterminal angle calculator! Works with degrees and radians to find out positive and negative coterminal angles!

Coterminal angle calculator

Table of contents

About coterminal angle calculator
How to use coterminal angle calculator?
What are coterminal angles?
What is the formula of coterminal angle?
How to calculate coterminal angle?
What are positive and negative coterminal angles?
What is terminal and initial side of an angle?
Are reference angles also coterminal angles?
What are the Coterminal Angles of 15°?
What are the Coterminal Angles of 30°?
What are the Coterminal Angles of 45°?
What are the Coterminal Angles of 60°?
What are the Coterminal Angles of 90°?
What are the Coterminal Angles of 120?
What are the Coterminal Angles of 180?

About coterminal angle calculator

A coterminal angle is the angle that has the same initial side and the same terminal sides. On this page you will learn all the essential formulas and information about coterminal angles. On this page you can calculate nearby coterminal angles for your given angle.

How to use coterminal angle calculator?

Add your given angle to coterminal angle calculator, and it will show you nearest coterminal angles.

What are coterminal angles?

The coterminal angles are the angles with the same initial side and terminal sides. They are determined by adding or subtracting 2π or 360° to the given angle. When the angle is moved, the terminal sides align at the same angle.
There can be found infinite number of coterminal angles for any given angle.

What is the formula of coterminal angle?

The coterminal angles of an angle can be calculated in degrees and radians.
For degrees, coterminal angle formula is:
θ ± 360 * n
For radians, coterminal angle formula is:
θ ± 2π * n
In the above formulas, n refers to a multiples of full rotations, which equals to 360 degrees or 2π.
Coterminal angle formula

How to calculate coterminal angle?

Calculating coterminal angle for given angle is simple. We can find the coterminal angles of any angle by adding multiples of 360 degrees or 2π to the the given angle.

What are positive and negative coterminal angles?

The coterminal angle can be a positive or negative.
Positive coterminal angles are angles that have the initial x-axis and their terminal side is determined by turning in a anti-clockwise direction.
Negative coterminal angles are angles that have the initial x-axis and their terminal side is determined by turning in a clockwise direction.
Positive and negative coterminal angles

What is terminal and initial side of an angle?

In mathematics an angle is a figure that is formed by two meetings at a common end point. The two sides that angle forms are called the initial and terminal sides.

Are reference angles also coterminal angles?

The reference angle is the smallest angle between the terminal arm and the x-axis. It is always positive and must be less than 90 degree.
So some coterminal angles can be reference angles if they meet the criteria, but as a default coterminal angles are not reference angles.
Reference angle

What are the Coterminal Angles of 15°?

Positive angles: 375°, 735°, 1095°, 1455°...
Negative angles: -345°, -705°, -1065°, -1425°...

What are the Coterminal Angles of 30°?

Positive angles: 390°, 750°, 1110°, 1470°...
Negative angles: -330°, -690°, -1050°, -1410°...

What are the Coterminal Angles of 45°?

Positive angles: 405°, 765°, 1125°, 1485°...
Negative angles: -315°, -675°, -1035°, -1395°...

What are the Coterminal Angles of 60°?

Positive angles: 420°, 780°, 1140°, 1500°...
Negative angles: -300°, -660°, -1020°, -1380°...

What are the Coterminal Angles of 90°?

Positive angles: 450°, 810°, 1170°, 1530°...
Negative angles: -270°, -630°, -990°, -1350°...

What are the Coterminal Angles of 120?

Positive angles: 480°, 840°, 1200°, 1560°...
Negative angles: -240°, -600°, -960°, -1320°...

What are the Coterminal Angles of 180?

Positive angles: 540°, 900°, 1260°, 1620°...
Negative angles: -180°, -540°, -900°, -1260°...

John Cruz
Article author
John Cruz
John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.

Coterminal Angle Calculator English
Published: Mon Aug 23 2021
In category Mathematical calculators
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