Enter the angle to find its coterminal angles using the calculator provided.
Coterminal Angles Calculation Formula
The following formulas are used to calculate the coterminal angles for a given angle:
Positive Coterminal Angle = Angle + 360°
Negative Coterminal Angle = Angle - 360°
Variables:
- Angle is the original angle in degrees (°)
- Positive Coterminal Angle is the angle found by adding 360°
- Negative Coterminal Angle is the angle found by subtracting 360°
To find the coterminal angles, simply add and subtract 360° from the given angle. This process can be repeated multiple times to find additional coterminal angles.
What are Coterminal Angles?
Coterminal angles are angles that share the same terminal side when drawn in standard position. This means that they are separated by an integer multiple of 360°, the full rotation in a circle. Coterminal angles have the same trigonometric functions values since they represent the same angle in the context of a circle.
How to Calculate Coterminal Angles?
Follow these steps to calculate coterminal angles:
- First, identify the given angle in degrees.
- To find the positive coterminal angle, add 360° to the given angle.
- To find the negative coterminal angle, subtract 360° from the given angle.
- For additional coterminal angles, continue to add or subtract multiples of 360°.
- Verify your results using the calculator above to ensure accuracy.
Example Problem:
Use the following variables as an example problem to test your knowledge:
Given Angle = 45°
FAQ
1. What is a coterminal angle?
A coterminal angle is any angle that differs from a given angle by a whole number multiple of 360°. For instance, 45° and 405° are coterminal because 405° is 45° plus 360°.
2. Why are coterminal angles important?
Coterminal angles are important in trigonometry because they have the same sine, cosine, and tangent values, making them useful in various applications, including solving trigonometric equations and analyzing periodic functions.
3. How can I find multiple coterminal angles?
To find multiple coterminal angles, you can keep adding or subtracting 360° (or 2π radians if you are working in radians) to the given angle. For example, for the angle 30°, coterminal angles include 390° (30° + 360°), 750° (30° + 2×360°), -330° (30° – 360°), etc.
4. Can coterminal angles be negative?
Yes, coterminal angles can be negative. For any given angle, you can find a negative coterminal angle by subtracting 360° from the angle. For example, the negative coterminal angle of 30° is -330°.
5. What if the angle is given in radians?
If the angle is given in radians, you find coterminal angles by adding or subtracting 2π radians. For instance, for an angle of π/3 radians, coterminal angles would be π/3 + 2π, π/3 – 2π, etc.