How do you evaluate tan(sin^-1(-5/11)) without a calculator?

1 Answer
Oct 11, 2016

--5/24sqrt 6.

Explanation:

Let a = sin^(-1)(-5/11) in Q_4, for the principal value.

Then, sin a = -5/11, cos a = sqrt(1-(-5/11)^2)= 4/11sqrt6

The given expression is

tan a = sin a/cos a= -5/(4sqrt 6)=-5/24sqrt 6

Of course, the general value a in Q_3 also. wherein tana is

positive and cos a is negative,

So, ignoring the principal-value-convention for inverse sine, the

answer could be presented as

=+-5/24sqrt6.

For me, this is the answer. You can choose yours.