• anonymous
Tan (sin^-1(-1))=____? A. undefined B. -1 C. 1 D. 0
  • schrodinger
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  • anonymous
Wait is it A. undefined ?
  • 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 \[\tan ( \sin^{-1}(-1)) = \tan(\theta)=?\]

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