# Coterminal Angle Calculator

## Table of Content

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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)

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.

Angle Positive Coterminal Angle Negative Coterminal Angle
0 360 -360
10 370 -350
20 380 -340
40 400 -320
60 420 -300
80 440 -280
100 460 -260
120 480 -240
140 500 -220
160 520 -200
180 540 -180
200 560 -160
220 580 -140
240 600 -120
260 620 -100
280 640 -80
300 660 -60
320 680 -40
340 700 -20
360 720 -360

## 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.

### Shaun Murphy

I'm graduated in biomedical and electrical engineering. Specialization in sports and medical topics but will gladly tackle everything you throw at him. He is a sailor, hiker, and motorcyclist in his free time.