coterminal angles
Angles which, drawn in standard position, share a terminal side. For example, 60°, -300°, and 780°
Coterminal angles are angles that have the same initial side and terminal side but differ by a multiple of 360 degrees. In simpler terms, if two angles have the same starting point (initial side) and end point (terminal side), and one of the angles is rotated a full 360 degrees or a multiple of 360 degrees, the resulting angle will be coterminal to the original angle.
For example, if we have an angle of 45 degrees, its coterminal angles can be found by adding or subtracting multiples of 360 degrees. So, 45 degrees and 405 degrees are coterminal angles, as are -315 degrees and 45 degrees.
Coterminal angles are important in trigonometry because they have the same trigonometric functions (sine, cosine, tangent, etc.) as their corresponding angles in standard position. This makes it easier to work with trigonometric functions, especially if we are working with angles that are greater than 360 degrees.
It’s important to note that coterminal angles can be positive or negative, depending on the direction of rotation from the initial side. We can also find coterminal angles by adding or subtracting 2π radians (which is equivalent to 360 degrees) from the original angle.