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Coterminal Angle Formula:
If result is negative, add 360° to find smallest positive equivalent
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Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. They differ by a multiple of 360° (or 2π radians) from each other.
The calculator uses the following formula:
If the result is negative, we add 360° to find the smallest positive equivalent angle.
Explanation: The modulo operation finds the remainder after division by 360, which gives us an equivalent angle between -360° and +360°. By adding 360° to negative results, we ensure the angle is between 0° and 360°.
Details: Coterminal angles are important in trigonometry because they share the same trigonometric function values (same sine, cosine, tangent, etc.). Finding the smallest positive coterminal angle simplifies calculations and standardizes angle measurements.
Tips: Enter any angle in degrees (positive or negative, whole number or decimal). The calculator will return the smallest positive equivalent angle between 0° and 360°.
Q1: What's the range of coterminal angles?
A: The smallest positive coterminal angle is always between 0° and 360°. All other coterminal angles can be found by adding or subtracting multiples of 360°.
Q2: Are coterminal angles the same as reference angles?
A: No, reference angles are always between 0° and 90° and represent the smallest angle between the terminal side and the x-axis.
Q3: How does this work for negative angles?
A: Negative angles rotate clockwise from the positive x-axis. The calculator automatically converts them to positive equivalents.
Q4: Can I find coterminal angles in radians?
A: Yes, the same principle applies but using 2π radians instead of 360°. This calculator works in degrees only.
Q5: Why is the smallest positive coterminal angle useful?
A: It provides a standardized way to represent angles that is often more convenient for calculations and comparisons.