What are the x-values where cos x equals 0?

The equation ( \cos x = 0 ) indicates the angles at which the cosine function takes on a value of zero. The cosine function equals zero at specific points along the unit circle.

These points occur at odd multiples of ( \frac{\pi}{2} ) radians, or in degrees, at ( 90^\circ + 180^\circ n ) where ( n ) is an integer. This means the cosine function equals zero at ( 90^\circ ) and ( 270^\circ ) within one complete cycle (0° to 360°). Extending beyond one cycle, it will also equal zero at angles like ( -90^\circ ) and ( -270^\circ ) as well as ( 450^\circ ) (which is ( 90^\circ + 360^\circ )) and ( 630^\circ ) (which is ( 270^\circ + 360^\circ )), and so forth.

Therefore, the correct x-values where ( \cos x = 0 ) includes ( \pm90^\circ ) and ( \pm270^\circ ), confirming that the answer provided is accurate. This set of angles captures all the