When Does Cos(x) = 0?

By Staff WriterLast Updated Apr 14, 2020 6:26:51 AM ET

The cosine of x is zero at values π/2, 3π/2, 5π/2, 7π/2 radians, and so on. Since this is a periodic function, cosine of x equals zero at these intervals on the unit circle, a circle of radius one that lies on the origin of the x-y axis.

The equation of the unit circle is x² + y² = 1. Translating radian values to x-y values requires use of the Pythagorean theorem, where x is the cosine value, and y is the sine value. The radian value π/2 makes a right angle, where the x value is equal to zero, and the y value is equal to one. Cosine is a trigonometric functions and occurs at cyclical intervals along a coordinate axis. Since cosine is cyclical, it will equal zero at regular intervals along the x-y axis and extend until infinity.