How to Find Coterminal Angles?

From the above explanation, for finding the coterminal angles:

• add or subtract multiples of 360° from the given angle if the angle is in degrees.
• add or subtract multiples of 2π from the given angle if the angle is in radians.

So we actually do not need to use the coterminal angles formula to find the coterminal angles. Instead, we can either add or subtract multiples of 360° (or 2π) from the given angle to find its coterminal angles. Let us understand the concept with the help of the given example.

Example: Find a coterminal angle of π/4.

Solution:

The given angle is θ = π/4, which is in radians.

So we add or subtract multiples of 2π from it to find its coterminal angles.

Let us subtract 2π from the given angle.

π/4 − 2π = −7π/4

Thus, a coterminal angle of π/4 is −7π/4.