# Why is cos(0) = 1?

Jun 28, 2015

In terms of the right triangles used to define trigonometric functions, cos(x) = frac{"adjacent side"}{"hypotenuse"}. When $x = 0$, $\text{adjacent side length" = "hypotenuse length}$. Therefore, $\cos \left(0\right) = 1$.

#### Explanation:

Consider a series of triangles with the base angle gradually approaching the value 0.

Feb 20, 2018

We can use the Unit Circle to prove this to ourselves:

#### Explanation:

At $0$ degrees, the angle intercepts the Unit Circle at the coordinate $\left(1 , 0\right)$. The coordinates are the trig values. The x-coordinate is the $\cos$ value and the y-coordinate is the $\sin$ value.