How do you evaluate #sec^-1(-2/sqrt3)#?

1 Answer
Annie
Aug 18, 2016

150 degrees or 5#pi#/3

Explanation:

sec#^-1# means the angle whose secant is -2/#sqrt3#
Which is the angle whose cosine is -#sqrt#3/2

Draw an equilateral triangle and cut in half.
The ratio of the sides of the right angle triangle are 1:2::#sqrt3#

So the angle whose cosine is +#sqrt3#/2 is 30 degrees or #pi#/3

From the cosine graph the angle whose cosine is-#sqrt3#/2 is 150 degrees or 5#pi#/3

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