Question

How do you use a calculator to evaluate `cos^-1 0.24` in both radians and degree?

Answer 1

76.113`@` and/or `(76133pi)/180000`

Explanation:

First i would get the degree by doing `cos^-1(0.24)` in a calculator to get 76.113`@`
This is `76.133` out of `360` which is `76.133/360`
Radians is out of `tau` or `2pi` To find out radian multiply the fraction by `tau` or `2pi` to get:
`76.133/360*2pi=(152.266pi)/360=(76133pi)/180000`

Answer 2

`x = 76^@, or (19pi)/45`
`x = 284^@, or (71pi)/45`

Explanation:

`cos ^-1 (0.24)` --> arccos (0.24)
Calculator and unit circle give -->
cos x = 0.24 -->
arc `x = +- 76^@`
For `(0, 360^@)` the answers are:
`x = 76^@` and
`x = 284^@` (co-terminal to `-76^@`)
Convert to radians:
`x = 76^@` --> `x = (76 pi)/180 = (19pi)/45`.
`x = 284^@` --> `x = (284pi)/180 = (71pi)/45`