# How To Find Coterminal Angle?

The study of trignometry is a branch of mathematics that focuses on the observation, assessment, and analysis of angles. It contains the functions of trigonometry as well as the operations of trigonometry in order to determine angles that are not known. Additionally, trigonometry has its own formulae for the many operations that may be performed, as well as conventional trigonometric values or ratios that apply to the sine, cosine, tangent, cotangent, secant, and cosecant functions when applied to a variety of angles.

The coterminal angles in trigonometry are the primary emphasis of the material that has been provided. The following information is included in the body of the article: a brief overview of coterminal angles and the many kinds of coterminal angles; the formula for coterminal angles; and the technique for determining it. There are also some example issues supplied so that you may better grasp the calculating procedure.

## Angles that are coterminous

The angles that share the same starting side and the same terminal side are referred to as conterminal angles. Coterminal angles take up a fixed location in each quadrant, which is what defines the range of values that they fall within. In trigonometry, coterminal angles are angles that have values that are the same for the sine, cosine, and tangent functions. When we encounter coterminal angles, we know that these angles are equivalent. In most cases, calculating these angles requires performing the mathematical operation of adding or subtracting 360 degrees or 2 degrees to the angle that has been supplied.

In the process of finding a coterminal angle, if the angles are rotated in either a clockwise or counterclockwise direction, they will coincide at the same terminal side. Coterminal angles may be either positive or negative, depending on how they are rotated.

## Positive coterminal angle

It is believed to be the positive coterminal angle when the rotation is counterclockwise and the value of n is discovered to be positive.

When the rotation is performed counterclockwise, the value of n in the expression 360n is positive.

**Coterminal angle that is to the negative**

It is believed to be the negative coterminal angle if the rotation goes in the clockwise direction and the value of “n” turns out to be negative.

When rotating in a clockwise direction, the value of n in the expression 360n takes on a negative sign.

## How can you identify angles that are coterminal?

## Answer:

The formula for derived coterminal angles, which makes use of the symbol ” as a reference for the operation, is what is used to calculate the coterminal angles. Therefore, the value of is necessary in order to calculate coterminal angles, regardless of whether the angles are measured in radians or degrees.

The formula for coterminal angles in mathematics is as follows:

In Degrees θ ± 360n

In Radian θ±2πn

Where,

The number n is the integer.

Coterminal angles may be measured in either degrees or radians, as was shown in the previous research done on this topic. And the multiples of the supplied number are written as 360n or 2n times themselves. Therefore,

To calculate the coterminal angle in degrees, you must first take the supplied angle and add or remove multiples of 360 from it.

Add or subtract multiples of 2 from the supplied angle in order to find the coterminal angles expressed in radians.

## Sample Problems

## Find the coterminal angle that corresponds to the value of /2.

## Solution:

Given:

The angle is expressed as = /2. (In radians)

Now,

To get the angle, multiply or divide by multiples of 2 degrees.

,

Take the angle that has been supplied and subtract 2 degrees from it.

=> π/2 – 2π

=> -3π/2

As a result, the angle that is coterminal with /2 is -3/2.

## Find the coterminal angle that corresponds to the value of /4.

## Solution:

Given:

The angle is calculated as = /4. (In radians)

Now,

To get the angle, multiply or divide by multiples of 2 degrees.

,

Let’s add two degrees to the existing angle.

=> π/4 + 2π

=> 9π/4

As a result, the angle that is coterminal with /4 is 9/4.

Determine the coterminal angle that corresponds to the value of /6.

Solution:

Given

The angle is defined as = /6. (In radians)

Now,

To get the angle, multiply or divide by multiples of 2 degrees.

,

Take the angle that has been supplied and subtract 2 degrees from it.

=> π/6 – 2π

=> -11π/6

As a result, the angle that is coterminal with /6 is -11/6.

## Find the angles that are coterminal with 30 degrees in the fourth question.

Solution:

Given:

The angle equals 30 degrees.

Let n equal one to go counterclockwise.

=> θ + 360n

=> 30 + 360 (1)

=> 390°

Let’s say n is equal to -2 for clockwise.

=> θ – 360n

=> 30 – 360 (-2)

=> -690°

## Find the angles that are coterminal to 40 degrees in the fifth question.

## Solution:

Given:

The angle equals 40 degrees.

Let n equal one to go counterclockwise.

=> θ + 360n

=> 40 + 360 (1)

=> 400°

Let’s say n is equal to -2 for clockwise.

=> θ – 360n

=> 40 – 360 (-2)

=> 40 – 720

=> -680°

## Find the angles that are coterminal with -450 degrees using the calculator below.

## Solution:

Given:

The angle equals -450 degrees.

Let n equal one to go counterclockwise.

=> θ + 360n

=> -450 + 360 (1)

=> -90°

Let’s say n is equal to -2 for clockwise.

=> θ – 360n

=> -450 – 360 (-2)

=> -450 – 720

=> -1170°