How do you find the exact value of #sin^-1(-0.5)#?

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Answer 1 · 2015-04-15T14:19:33

When asked to evaluate inverse trigonometric functions, first ask yourself, "Is the answer a special angle?"

#sin^-1(-0.5) = sin^-1(-1/2)#

Is there a special angle with #sint = 1/2#?

Yes, #t= pi / 6#.

But we want #sint = -1/2#, so we want an answer in quadrant 3 or 4.

#sin^-1(x)# always gives us a #t# between #-pi/2# and #pi/2#, so we want #t = - pi/6#

#sin^-1(-0.5) = pi/6#