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

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Answer 1 · 2016-10-11T15:50:26

#--5/24sqrt 6#.

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.