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Coterminal Angle Calculator

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This coterminal angle calculator allows you to calculate the positive and negative coterminal angles for the given angle and also clarifies whether the two angles are coterminal or not.

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 Angle

Positive and Negative Coterminal Angles:

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°

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

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.

How Coterminal Angle Calculator Works?

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 angles calculator will also simply tell you if two angles are coterminal or not.

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.