How do you simplify #sin (tan^-1 (-3))#?

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Answer 1 · 2016-07-08T08:04:15

#-3/sqrt 10#, for principal value of #tan^(-1)(-3)#. The general solution is #+-3/sqrt 10#.

Let #a=tan^(-1)(-3)#. Then, #tan a = -3<0#.

So, the principal a is in the fourth quadrant and the general a is in

either fourth or second.

And so, #sin a = -3/sqrt 10# against principal a and the given

expression

#sin a=-3/sqrt 10#

The general solution is # +-3/sqrt 10#.