Why are there an infinite number of angles that are co terminal to a certain angle?

Answer 1

There are an infinite number of angles that are coterminal with a given angle because coterminal angles differ by full rotations. Specifically, for any angle ( \theta ), you can find coterminal angles by adding or subtracting multiples of ( 360^\circ ) (or ( 2\pi ) radians). This means that ( \theta + 360^\circ n ) (where ( n ) is any integer) will always result in an angle that shares the same terminal side as ( \theta ), leading to an infinite set of such angles.