# How to find the value of x if #sec x = -5#?

##### 1 Answer

We rewrite the secant function and do some algebric manipulation.

We take the arccosine of both sides

And evaluate that on a calculator, it comes out to approximately

The arccosine has a proper range so it outputs every value uniquely (We know it only outputs values on the range of

But since we know that

Where

And that isn't all done, since there is another angle, this time on the third quadrant with the same cosine, we know that

Therefore,

Which leaves us