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

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Question 169169: Find the exact value of the expression. sec^-1(-2)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=sec%5E%28-1%29%28-2%29. So this means that sec%28x%29=-2 which further tells


sec%28x%29=-2 Start with the given equation


1%2Fcos%28x%29=-2 Replace secant with 1%2Fcosine. 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.


1=-2cos%28x%29 Multiply both sides by cos%28x%29


-1%2F2=cos%28x%29 Divide both sides by -2


arccos%28-1%2F2%29=x Take the arccosine (or inverse cosine) of both sides to isolate x



x=-pi%2F3 or x=2pi%2F3 Take the arccosine of -1%2F2 to get -pi%2F3 or 2pi%2F3


Since it was stated above that the angle had to be in quadrants 2 or 3, this means that we can ignore x=-pi%2F3



So x=2pi%2F3 which means that sec%5E%28-1%29%28-2%29=2pi%2F3