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

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Answer 1 · 2016-08-18T14:27:23

150 degrees or 5 $pi$ /3

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

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