Question

At which angle is secant of theta equals negative radical 2 question mark

Answer 1

The equation is given to be:

`\sec\theta=-√(2)`

Recall that sec is the inverse of cos. Thus, we have:

`(1)/(\cos\theta)=-√(2)`

Rewriting the equation, we have:

`\cos\theta=-(1)/(√(2))`

We can find the arccos of both sides:

`\theta=\arccos(-(1)/(√(2)))`

Since we know that:

`\cos(-x)=\cos(x)`

Then, we have:

`\theta=\arccos((1)/(√(2)))`

Recall the identity:

`\arccos((1)/(√(2)))=(3\pi)/(4)+2\pi n,\:θ=(5\pi)/(4)+2\pi n`

Therefore, the answer is the SECOND OPTION.