## anonymous one year ago Tan (sin^-1(-1))=____? A. undefined B. -1 C. 1 D. 0

1. anonymous

Wait is it A. undefined ?

2. Kainui

What you put into a trig function is an angle and out of it you get a ratio of sides. So the inverse of a trig function takes ratios of sides and gives you an angle! To make our lives simpler, I will do that: $\tan ( \sin^{-1}(-1))$ See, that arcsine in there is giving us an angle: $\theta = \sin^{-1}(-1)$ We can turn it inside out by taking sine of both sides: $\sin(\theta) = -1$ So now what value of $$\theta$$ gives us this answer? Once you figure this out you can plug it in based on our substitution to find out what $\tan ( \sin^{-1}(-1)) = \tan(\theta)=?$