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

At which angle is secant of theta equals negative radical 2 question mark-example-1

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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.

User Luatic
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