Coterminal Angle Calculator

With this coterminal angle calculator, you'll find some positive and negative coterminal angles, as well as the coterminal angle in the 0-360° (0-2π) range. Moreover, this tool is useful for checking if two angles are coterminal.

What is a Coterminal Angle?

“The angle in a standard position which has common terminal sides is known as coterminal angle”. 

It is an angle with the initial side on the positive x-axis having their terminal sides at the same location. Every angle has an infinite number of coterminal angles same as the angles 30°, –330°, and 390° are all coterminal. Solve your coterminal issues by taking the help of a coterminal angles calculator. 

Coterminal Angle Formula: 

Keep in mind that if there are two angles and their difference of degree measures is divisible by 360° and in the case of radian 2π then these are coterminal. So check out whether the angles α and β are terminals or not by the below formula:

In Case of Degree:

β = α ± (360°×k)

In Case of Radian:

β = α ± (2π×k)

These angles are determined by subtracting or adding a complete circle to the given angle or using a coterminal angle calculator.

• The starting position of the ray is the initial side of an angle 
• The position after rotation is their coterminal angle 
• Coterminal angles have the same trigonometric values 

Positive and Negative Coterminal Angles:

Coterminal angles may be positive or negative and involve the rotation of multiples of 360°. You'll find positive and negative angles and also the angle in the range of 0-360° (0-2π) in the below table. 

The below chart will help you to understand how to find coterminal angles and allow you to compute these angles in different values. 

Example:

Find out the coterminal angle of 350°.

Given Angle = 350 degree

As we already have discussed above angles are determined by subtracting or adding a 360° or 2π to the given angle.

Positive Coterminal Angles: 710°, 1070°, 1430°, 1790° ....

Negative Coterminal Angles: -10°, -370°, -730°, -1090° ....

350° = 35/18 

π ≈ 1.944 π

Working of Coterminal Angle Calculator:

This online gadget allows for evaluation that returns exact values and steps given either a degree or radian value. You can put the values below in it and it will function properly.

Input:

• Choose what you want to calculate (find coterminal angles, and check whether two angles are coterminal or not)
• Set degree or radian from the designated field  
• Put the angle value 
• Tap “Calculate”

Output:

Our coterminal angle calculator will evaluate the following results

• Positive and negative coterminal angle 
• Find that two angles are coterminal or not

References:

From the source of Varsity Tutors: Coterminal Angles, negative angle coterminal, Standard position.

From the source owlcation: Coterminal Angles, How to Find the Coterminal Angles in Radians and Degrees, Example 1: Finding Coterminal Angles and Classifying by Quadrant.