SOLUTION: Find the exact value of the expression. sec^-1(-2)

Question 169169: Find the exact value of the expression. sec^-1(-2)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let . So this means that which further tells

Start with the given equation

Replace secant with . Take note that cosine is negative (since 1 divided by a negative number is negative). This means that the angle MUST be in either the 2nd or 3rd quadrants.

Multiply both sides by

Divide both sides by -2

Take the arccosine (or inverse cosine) of both sides to isolate x

or Take the arccosine of to get or

Since it was stated above that the angle had to be in quadrants 2 or 3, this means that we can ignore

So which means that

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