Question

PLEASE HELP PLEASE HELP ASAP ASAP .

Answer 1

`\cos^(-1) (-(√(2) )/(2)) = 135^\circ`

Explanation:

Let us assume that
`\theta = \cos^(-1) (-(√(2) )/(2))`

⇒
`\cos \theta = -(√(2) )/(2) = - (1)/(√(2) )` ........... (1)

So, the
`\cos \theta` value is negative in the second and third quadrant and we know that
`\cos 45 = (1)/(√(2))`.

Therefore,
`\theta = \pi + (\pi )/(4)` or
`\theta = \pi - (\pi )/(4)`

And the general solution of equation (1) is given by

`\theta = (2n + 1)\pi \pm (\pi )/(4)` for n = 0, 1, 2, ....

Since we need a definite solution of
`\theta` in the second quadrant, hence,
`\theta = \pi  - (\pi )/(4) = 135^\circ`. (Answer)