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Coterminal Angle Calculator

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Use this online coterminal angle calculator that allows you to calculate the positive and negative coterminal angles for the given angle. Also, the coterminal calculator clarifies whether the two angles are coterminal or not. So, keep reading to make out how to find coterminal angles in radians or degrees, coterminal angles formula, and coterminal angle definition.

What is a Coterminal Angle?

Coterminal angles are those angles that share the same initial and terminal sides. Their angles are drawn in the standard position in a way that their initial sides will be on the positive x-axis and they will have the same terminal side like 110° and -250°.

According to the coterminal definition:

  • The initial side of an angle will be the point from where the measurement of an angle starts.
  • Whereas The terminal side of an angle will be the point from where the measurement of an angle finishes.

Coterminal Angles Calculator

Furthermore, use an Area Between Two Curves Calculator to determine the area between two curves on a given interval corresponding to the difference between the definite integrals.

Positive and Negative Coterminal Angles:

For finding positive and negative coterminal angles, you can try our coterminal angle calculator. Apart from this, you have to subtract or add a number of complete circles as follows:

By adding and subtracting a number of revolutions, you can find any positive and negative coterminal angle. For example, if the chosen angle is: α = 14°, then by adding and subtracting 10 revolutions you can find coterminal angles as follows:

  • For positive coterminal angle: β = α + 360 = 14° + 360° = 374°
  • For negative coterminal angle: β = α – 360 = 14° – 360° = -346°

When finding the positive and negative coterminal angles, always remember that the revolutions must be large enough to reverse the sign. For example, if you have one revolution then it will be not enough to give you a negative coterminal angle and you will just get two positive angles, 15°, and 13°.

Coterminal Angles Formula:

Coterminal angles of any given angle can be calculated by using the following formula:

  • Coterminal of θ = θ + 360° × k (if θ is in degrees).
  • Coterminal of θ = θ + 2π × k (if θ is in radians).

However, you can use a coterminal angle calculator instead of applying a formula for the calculation of all the possible coterminal angles. Always keep in mind that Two angles will be coterminal if the difference among them is a multiple of 360° or 2π.

Moreover, an online Slope Calculator helps to find the slope (m) or gradient between two points in the Cartesian coordinate plane.

How to find coterminal angles (Step-by-Step)?

To find coterminal angles in steps follow the following process:

  • If the given an angle in radians (3.5 radians) then you need to convert it into degrees:
  • 1 radian = 57.29 degree so 3.5*57.28=200.48 degrees
  • Now you need to add 360 degrees to find an angle that will be coterminal with the original angle:
  • Positive coterminal angle: 200.48+360 = 560.48 degrees.
  • Negative coterminal angle: 200.48-360 = 159.52 degrees

However, a Coterminal Angles Calculator can be used to verify the answers of manual calculations to check its accuracy and functionality.

Example 1: 

Determine the coterminal angle of π/4

Solution:

Given Angle: θ = π/4,

Which is in radians,

So, multiples of 2π add or subtract from it to compute its coterminal angles.

Now, subtract 2π from the angle.

= π/4 − 2π

= −7π/4

Hence, the coterminal angle of π/4 is equal to −7π/4.

Example 2: 

Determine the positive and negative coterminal angle with a 495° angle.

Solution:

495°−360°= 180 – 135°= 45°

A 135° angle and a 495° angle are coterminal with the 45° angle.

How Coterminal Angle Calculator Works?

The coterminal angles calculator helps you to calculate coterminal angles and supports you to determine that if the two angles are coterminal or not. Follow the steps given below:

Input:

  • First of all, select the option “find coterminal angles” or “check two angles are terminal or not” in the drop-down menu.
  • Now Select degrees or pi radians
  • Enter the given angle to find the coterminal angles or two angles to verify coterminal angles.
  • Hit the calculate button

Output:

  • Positive coterminal angles will be displayed
  • Negative coterminal angles will be displayed
  • The coterminal angle calculator will also simply tell you if two angles are coterminal or not.

FAQs:

Why are Coterminal Angles Important?

In trigonometry, there are functions of angles such as sin, cos, and tan. Coterminal angles have the same value for all the trigonometric functions. So they are important because of this simplification.

What is meant by Standard Angle?

The Angle that is present in a coordinate plane and has a vertex at the origin and initial arm towards the positive x-axis will be known as an angle of the standard position.

What is the Reference Angle For?

We use the reference angle for the simplification of the calculations in the trigonometric function value for various angles. For the larger angles, it should be less than 90 degrees.

Can an Angle be Coterminal with Itself?

Yes! Any angle can be coterminal with itself no matter whether it is in radians or degrees. Use a coterminal calculator to check if the angle is coterminal with itself or not.

Takeaway:

This coterminal angle calculator will help you solve problems related to calculating the coterminal angle. It is a multifunctional calculator that can help you in education and academic research. In addition, the answer is displayed in seconds, so you can rely on this calculator for fast and accurate calculations.

Reference: 

From the source of Wikipedia: Etymology, coterminal, Adjective, Initial and terminal objects.

From the source of Varsity Tutors: Coterminal Angles, negative angle coterminal, Standard position.

From the source of Open Math: Either or both angles can be negative, two angles are coterminal, Why is this important?