ITF - Inverse Sine Lesson

Math_Lesson_TopBanner.png Inverse Sine

In previous courses, you've learned about Functions and their Inverses.

Here are some important points to review:

  • An inverse relation switches the input and output!
  • An inverse relation is a function if the original function is one-to-one.
  • In a one-to-one function each y­­-value is paired with exactly one x-value.

Watch this video to get an idea of how we will restrict the domain of LaTeX: f\left(x\right)=\sin x\:to\:create\:f^{\:-1}\left(x\right)=\sin^{-1}xf(x)=sinxtocreatef−1(x)=sin−1x.

So, now that you understand where LaTeX: f\left(x\right)=\sin^{-1}xf(x)=sin−1x is. It is important to know some of these facts:

  1. We can call the inverse function LaTeX: f\left(x\right)=\sin^{-1}x\:or\:f\left(x\right)=arc\:\sin xf(x)=sin−1xorf(x)=arcsinx.
  2. The domain of LaTeX: f\left(x\right)=\sin^{-1}xf(x)=sin−1x is [-1, 1].
  3. The range of LaTeX: f\left(x\right)=\sin^{-1}x\:is\:\left[-\frac{\Pi}{2},\:\frac{\Pi}{2}\right]f(x)=sin−1xis[−Π2,Π2]

inverse sine cycle sine(angle)=ratio sine to -1(ratio)=angle The input becomes the output the output becomes the input

image of a sine unit circle indicating positive sine and negative sine

Watch this video to practice a few more problems:

Try these problems to check your understanding:

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