# How is cos (-x) = cos x?

We need to know how is cos(-x) = cos x

### Solution

Cosine and sine values are complementary, Thus cos a = sin (90-a).

cos (-x) = sin (90+x) { using th identity cos )A + B)}

= sin 90 cos x + cos 90 sin x

= 1*cos x + 0

= cos x

It’s the same given number or angle.

### Explanation

Starting from the point (1,0) on the on the unit circle, which is when we have an angle of 0 raidans. On moving along the circumference of the circle, and running the same angle, a first time counterclockwise, and a second time clockwise. The two angles are Θ and -Θ. We end up with two points which lie on the same vertical line, which means that one is the reflection of the other with respect to the X axis. It shows that the two points have coordinates (x,y) and (x,-y). Since the cosine is the x-coordinate of the points on the unit circle, you see that the two points have the same cosine, and opposite sine.

The cosine is an even function, which means exactly that cos(-x) = cos x.