To find coterminal angles, add or subtract 360° from the given angle for positive and negative coterminal angles, respectively.
The Coterminal Angle Calculator enables you to identify angles that share the same terminal side, differing only by full rotations (360° in degrees). Coterminal angles are useful in trigonometry for simplifying angle measures in calculations.
By knowing the positive and negative coterminal angles, you can express any angle in an equivalent form that falls within standard ranges.
Formula
Positive Coterminal Angle = Angle + 360°
Negative Coterminal Angle = Angle − 360°
| Variable | Description |
|---|---|
| Angle | Given angle in degrees |
| Positive Coterminal Angle | Equivalent positive angle |
| Negative Coterminal Angle | Equivalent negative angle |
Solved Calculations
Example 1:
| Step | Calculation |
|---|---|
| Given Angle | 45° |
| Positive Coterminal | |
| Result | 405° |
| Negative Coterminal | |
| Result | -315° |
Answer: For an angle of 45°, the positive coterminal angle is 405°, and the negative coterminal angle is -315°.
Example 2:
| Step | Calculation |
|---|---|
| Given Angle | 200° |
| Positive Coterminal | |
| Result | 560° |
| Negative Coterminal | |
| Result | -160° |
Answer: For an angle of 200°, the positive coterminal angle is 560°, and the negative coterminal angle is -160°.
What is a Coterminal Angle Calculator?
The Coterminal Angle Calculator is a useful angle-finding tool. In particular, it finds the angles that share the same terminal side as a given angle, either in degrees or radians. Coterminal angles are calculated by adding or subtracting full rotations (360° or radians) from the original angle, allowing you to find angles that end at the same position on a coordinate plane.
This can be particularly helpful in trigonometry for simplifying calculations and analyzing periodic functions.
To rely on this calculator, merely input your initial angle. The calculator will then provide both positive and negative coterminal angles, offering the smallest positive coterminal angle and the largest negative coterminal angle within the 0° to 360° range or 0 to radians.
Final Words:
In a word, the Coterminal Angle Calculator is a handy tool for students and professionals alike, simplifying the process of finding equivalent angles and aiding in various trigonometric and geometric calculations.
