Question

Why is cos(0) = 1?

Answer 1

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

Explanation:

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

Answer 2

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

Explanation:

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