TEF - Inverse Cosine Lesson

Inverse Cosine

Let's review a little bit of information about equation image indicator $LaTeX: f\left(x\right)=\cos x$ $f\left(x\right)=\cos x$ .

1. What is the domain of equation image indicator $LaTeX: f\left(x\right)=\cos x$ $f\left(x\right)=\cos x$ ?

Solution: all real numbers

2. What is the range of equation image indicator $LaTeX: f\left(x\right)=\cos x$ $f\left(x\right)=\cos x$ ?

Solution: [-1, 1]

Watch this video to get an idea of how we will restrict the domain of equation image indicator $LaTeX: f\left(x\right)=\cos x,\:$ $f\left(x\right)=\cos x,\:$ to create $LaTeX: f^{-1}\left(x\right)=\cos^{-1}x$ $f^{-1}\left(x\right)=\cos^{-1}x$ .

So, now that you understand where equation image indicator $LaTeX: f\left(x\right)=\cos^{-1}x$ $f\left(x\right)=\cos^{-1}x$ it is important to know some of these facts:

We can call the inverse function $LaTeX: f\left(x\right)=\cos^{-1}x$ $f\left(x\right)=\cos^{-1}x$ or $LaTeX: f\left(x\right)=arc\cos x$ $f\left(x\right)=arc\cos x$ .
The domain of $LaTeX: f\left(x\right)=\cos^{-1}x$ $f\left(x\right)=\cos^{-1}x$ is [-1, 1].
The range of $LaTeX: f\left(x\right)=\cos^{-1}x$ $f\left(x\right)=\cos^{-1}x$ is $LaTeX: \left[0,\:\pi\right]$ $\left[0,\:\pi\right]$ .

cosine inverse function cycle
cos(angle)=ratio
cos to -1(ratio)=angle
the input becomes the output
the output becomes the input

cosine unit circle indicating a negative cosine and positive cosine

Watch this video to practice a few more problems:

Try these problems to check your understanding:

IMAGES CREATED BY GAVS