The two angles are said to be coterminal angles if their sum is multiples of 360o sharing the same terminal side. In the figure below 150o, -210o are coterminal angles.

To calculate the positive coterminal angle and negative coterminal angle we add and subtract 360o by the given angle.

Coterminal angle Calculator is a online tool which calculates the coterminal angles instantly. Provided is the block where you are supposed to enter the angle to get the two possible  and negative coterminal angles respectively.

## Coterminal Angle Problems

Here are the steps to get the coterminal angles
Step 1 : Read the problem and Note down the given angle $\theta$.

Step 2 : Calculate the coterminal angle use the formula
Positive Coterminal angle = $\theta$ + n(360o)
Negative Coterminal angle = $\theta$ - n (360o)
Substitute the value of $\theta$ to get the desired multiples (n) of coterminal angles.

Below are given some problems based on Coterminal angles which may be helpful for you.

### Solved Examples

Question 1: Find the two smallest positive angles which is coterminal with 30o.
Solution:

The given angle is $\theta$ = 30o.
The two Positive coterminal angle is given by

$\theta$ + 360o = 30o + 360o = 390o
$\theta$ + 2(360o) = 30o + 720o = 750o.

Hence 390o and 750o are two angles coterminal with 30o.

Question 2: Find the two smallest negative coterminal angles for 90o.
Solution:

The given angle is $\theta$ = 90o
The two Negative coterminal angle is given by

$\theta$ - 360o = 90o - 360o = - 270o
$\theta$ - 2(360o) = 90o - 720o = - 630o.

Hence -270o and -630o are two angles coterminal with 90o.

### Reference Angle Calculator

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