coterminal angles

Coterminal angles share the same terminal and initial sides. Determining a coterminal angle is as easy as subtracting or adding 2π or 360° to each angle, which depends upon whether the angle is in radians or degrees. There are infinite numbers of coterminal angles that can be found. Here’s the procedure for finding coterminal angles, otherwise you can use a handy coterminal angle calculator. This is the most popular method for finding trigonometric equations which will be done in the future.

So, radians are commonly used in trigonometry to designate angle measures. The measurements in radians are easy to understand and very common in calculus, therefore it is crucial to have an understanding of what a radian is, so a coterminal radians calculator can help you to determine the measurements of several angles in radian.

Well, if we take the length of the radius of a particular circle, and lay it on the edge of the circle, that length would be a radian.

Methods of Finding Coterminal

To find coterminal mathematically by subtracting number 360 until the number 0 to 360 can be reached. Apart from this, if the angle is -ve add 360 until a number between 0 and 360 is reached.

-330° + 360 = 30 so, -330° and 30° are coterminal

390° – 360 = 30 so, 390° and 30° are coterminal

Also, you can find these angles by using a coterminal angle calculator. An angle is in standard position if it is drawn on the x-y plane, on the +ve x-axis, and turning anti-clockwise.

The start site is a ray where the calculation of an angle starts. And the terminal side is a ray where the measurements of angle end. Coterminal angles, when drawn at standard position, share a terminal side. 

For example, 30°, -315°, 405° are all coterminal.

Identifying Coterminal Angles

According to the coterminal angle definition, two angles are coterminal when they have a similar terminal side. You have to use a coterminal angle calculator to give an angle measure for a specific terminal ray. Generally, using a -ve angle rather than a +ve angle is more efficient, because angles can have terminal sides that relate to one or more spins around the terminal sides of origin that go clockwise instead of anticlockwise, or both of these situations can happen.

Negative Coterminal Angles

An angle of 110 degrees is coterminal with an angle of –250 degrees. Therefore, with the coterminal formula Two rotations in the negative (clockwise) direction give you an angle of –710 degrees (–250 – 360 = –710).

Coterminal Angle Examples:

Determine the following angles are coterminal or not.

a) 110°, 470°

b) -260°, -460°

c) –800°, –60°


a) 110° – 470° = 360° = 1(360°), which is a multiple of 360°

So, 110° and 470° are coterminal

b) -260° – 460° = –720° = –2(360°), which is a multiple of 360°

So, –260 and -460° are coterminal

c) –800° – (–60°) = –860°, which is not a multiple of 360°

So, –800° and –60° are not coterminal, hence, you can find the angles are coterminal or not with the coterminal angle calculator.

By Anurag Rathod

Anurag Rathod is an Editor of, who is passionate for app-based startup solutions and on-demand business ideas. He believes in spreading tech trends. He is an avid reader and loves thinking out of the box to promote new technologies.