Coterminal Angles Calculator

Coterminal Angles Calculator is an online tool that helps to calculate the positive and negative coterminal angles of the specified angle. Angles that have the same initial side and the same terminal side are known as coterminal angles.

What is Coterminal Angles Calculator?

Coterminal Angles Calculator helps to compute the positive and negative coterminal angles of a given angle that is expressed in degrees. To determine a coterminal angle we add or subtract 360 degrees from it. To use the coterminal angles calculator, enter the angle in the given input box.

Coterminal Angles Calculator

NOTE: Enter upto three digits only.

How to Use Coterminal Angles Calculator?

Please follow the steps below to find the coterminal angles of the given angle using the coterminal angles calculator:

• Step 1: Go to Cuemath's online coterminal angles calculator.
• Step 2: Enter the angle in the given input box of the coterminal angles calculator.
• Step 3: Click on the "Calculate" button to find the coterminal angles.
• Step 4: Click on the "Reset" button to clear the fields and enter new values.

How Does Coterminal Angles Calculator Work?

Angles that occupy the same position even if they have differing values are known as coterminal angles. Their vertices are identical and they occupy the same side on the same quadrant. A coterminal angle can be formed when a specified angle is rotated clockwise or anti-clockwise and its terminal side coincides. The original position of the ray is known as the initial side and the final position of the ray is called its terminal side. If the difference between two angles results in the multiple of 360 degrees then the two angles will be coterminal to each other. The steps given below can be used to find both the positive and negative coterminal angles of a given angle, θ.

1. Positive Coterminal Angles

• Add multiples of 360 degrees to the given angle. θ + 360, θ + 720, .... will be the positive coterminal angles of θ.
• If θ is given in radians then we add multiplies of 2π to it, so as to find the positive coterminal angles.

1. Negative Coterminal Angles

• Subtract multiples of 360 degrees from the given angle. θ - 360, θ - 720, .... will result in the negative coterminal angles of θ.
• To find the negative coterminal angles when θ is expressed in radians, we subtract multiples of 2π from θ.

Solved Examples on Coterminal Angles

Example 1: Find coterminal angles for 60° and verify them using the coterminal angles calculator.

Solution:

Given angle = 60°

Positive coterminal angles of 60° are 60° + 360°, 60° + 720°, 60° + 1080°...

= 420°, 780°, 1140°...

Negative coterminal angles of 60° are 60° - 360°, 60° - 720°, 60° - 1080°...

= -330°, -660°, -1020°...

Example 2: Find coterminal angles for -25° and verify them using the coterminal angles calculator.

Solution:

Given angle = -25°

Positive coterminal angles of -25° are -25° + 360°, -25° + 720°, -25° + 1080°...

= 335°, 695°, 1055°...

Negative coterminal angles of 60° are -25° - 360°, -25° - 720°, -25° - 1080°...

= -385°, -745°, -1105° ...

Similarly, you can try the coterminal angles calculator to find the coterminal angles for

• Angle 45°
• Angle -34°