Question

What is the inverse cosine of 1?

Answer 1

The inverse cosine of 1 is 0 (or any integer multiple of `2pi`)

Explanation:

Inverse cosine = arccos = cos^(-1)

If `arccos(1) = theta`
then `cos(theta)=1color(white)("XXXX")`by definition.

If `cos(theta)=1`
then based on the unit circle definitions of trigonometric functions:
`color(white)("XXX")"adjacent side"/"hypotenuse" = 1`

i.e.`color(white)("XX")"adjacent side" = "hypotenuse"`

The only location where this is true is when `theta=0` (or some multiple of full rotations that places the hypotenuse back on the positive X-axis).