How do you evaluate $cot [sin^-1 (- sqrt2 / 3)]$ ?

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Answer 1 · 2016-05-20T02:51:53

$+-sqrt (7 / 2)$

Let $a = sin^(-1)-sqrt 2 / 3$ . Then, $sin a=-sqrt 2 / 3<0$ .

Accordingly, a is in the 3rd quadrant or in the 4th.

So, $cos a = +-sqrt(1-sin^2a)=+-sqrt 7 / 3$ .
The answer is $cot a = cos a/sin a = +- sqrt (7/2)$ .

How do you evaluate cot [sin^-1 (- sqrt2 / 3)]cot [sin^-1 (- sqrt2 / 3)]?