Question

How do you calculate `cos^-1 (-0.8)`?

Answer 1

`theta=143.13^@`or `216.87^@`

Explanation:

Since -0.8 is not a value you would find in a trigonometric ratio, which are: `sintheta`, `costheta`, `tantheta`, `csctheta`, `sectheta`, `cottheta`, you have to use a calculator to find the answer:

`costheta=-0.8`
`color(white)(xx)theta=cos^-1(-0.8)`
`color(white)(xxx)~~143.13^@`

However, according to the CAST rule, cosine is also negative in the third quadrant, which means there is a second possible answer.

First, find the related acute angle, and add the angle to `180^@` to find the second possible answer.

Finding the related acute angle
`180^@-143.13^@`
`=36.87^@`

Finding the second possible angle
`=180^@+36.87^@`
`=216.87^@`

`:.`, the two possible angles are `143.13^@` and `216.87^@`.