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

Question

asked Sep 20, 2023 182k views

1 Answer

Luatic · Answer 1 · 2023-09-25T17:45:43+0000

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.