Question

HELP FAST PLS QUICK!!!!

Answer 1

`√(2)`

Explanation:

we know that

`tan^(2)(\theta)+1=sec^(2)(\theta)`

we have

`tan^(2)(\theta)=-1`

substitute the value

`(-1^(2))+1=sec^(2)(\theta)`

`(1)+1=sec^(2)(\theta)`

`sec^(2)(\theta)=2\\ \\sec(\theta)=(+/-)√(2)`

Remember that

The angle theta belong to the III and IV quadrant, but the tangent is negative, therefore belong to the IV quadrant

so

`sec(\theta)` is positive

therefore

`sec(\theta)=+√(2)`