Slope calculator With this coterminal angle calculator, you'll find some positive and negative coterminal angles, as well as the coterminal angle in the 0-360° (0-2π) range. Moreover, this tool is useful for checking if two angles are coterminal.
What is a Coterminal Angle?
“The angle in a standard position which has common terminal sides is known as coterminal angle”.
It is an angle with the initial side on the positive x-axis having their terminal sides at the same location. Every angle has an infinite number of coterminal angles same as the angles 30°, –330°, and 390° are all coterminal. Solve your coterminal issues by taking the help of a coterminal angles calculator.
Coterminal Angle Formula:
Keep in mind that if there are two angles and their difference of degree measures is divisible by 360° and in the case of radian 2π then these are coterminal. So check out whether the angles α and β are terminals or not by the below formula:
In Case of Degree:
β = α ± (360°×k)
In Case of Radian:
β = α ± (2π×k)
These angles are determined by subtracting or adding a complete circle to the given angle or using a coterminal angle calculator.
- The starting position of the ray is the initial side of an angle
- The position after rotation is their coterminal angle
- Coterminal angles have the same trigonometric values
Positive and Negative Coterminal Angles:
Coterminal angles may be positive or negative and involve the rotation of multiples of 360°. You'll find positive and negative angles and also the angle in the range of 0-360° (0-2π) in the below table.
The below chart will help you to understand how to find coterminal angles and allow you to compute these angles in different values.
| Angle | Positive Coterminal Angle | Negative Coterminal Angle |
|---|---|---|
| 0 | 360 | -360 |
| 10 | 370 | -350 |
| 20 | 380 | -340 |
| 40 | 400 | -320 |
| 60 | 420 | -300 |
| 80 | 440 | -280 |
| 100 | 460 | -260 |
| 120 | 480 | -240 |
| 140 | 500 | -220 |
| 160 | 520 | -200 |
| 180 | 540 | -180 |
| 200 | 560 | -160 |
| 220 | 580 | -140 |
| 240 | 600 | -120 |
| 260 | 620 | -100 |
| 280 | 640 | -80 |
| 300 | 660 | -60 |
| 320 | 680 | -40 |
| 340 | 700 | -20 |
| 360 | 720 | -360 |
Example:
Find out the coterminal angle of 350°.
Given Angle = 350 degree
As we already have discussed above angles are determined by subtracting or adding a 360° or 2π to the given angle.
Positive Coterminal Angles: 710°, 1070°, 1430°, 1790° ....
Negative Coterminal Angles: -10°, -370°, -730°, -1090° ....
350° = 35/18
π ≈ 1.944 π
Working of Coterminal Angle Calculator:
This online gadget allows for evaluation that returns exact values and steps given either a degree or radian value. You can put the values below in it and it will function properly.
Input:
- Choose what you want to calculate (find coterminal angles, and check whether two angles are coterminal or not)
- Set degree or radian from the designated field
- Put the angle value
- Tap “Calculate”
Output:
Our coterminal angle calculator will evaluate the following results
- Positive and negative coterminal angle
- Find that two angles are coterminal or not
References:
From the source of Varsity Tutors: Coterminal Angles, negative angle coterminal, Standard position.
From the source owlcation: Coterminal Angles, How to Find the Coterminal Angles in Radians and Degrees, Example 1: Finding Coterminal Angles and Classifying by Quadrant.