How to Graph Inverse of the Cosine Function?

A step-by-step guide to graphing the inverse of the cosine function

The inverse cosine function is the inverse of the cosine function. \(cos\) inverse \(x\) can also be written as \(\:arccos\:x\). If \(y=cos\:x\:⇒\:x=cos^{-1}\left(y\right)\)

Since the domain and range of the inverse \(cos\) function are \([-1, 1]\) and \([0, π]\), respectively, we will plot the graph of cos inverse x on the main branch. As we know the values of the \(cos\) function for certain angles, we use the same values to plot the points and thus the inverse \(cos\) graph. For \(\:y=cos^{-1}x\), we have:

• When \(x = 0\rightarrow\) \(y = \frac{π}{2}\)
• When \(x = \frac{1}{2}\rightarrow y = \frac{π}{3}\)
• When \(x = 1\rightarrow y = 0\)
• When \(x = -1\rightarrow y = π\)
• When \(x = -\frac{1}{2}\rightarrow y = \frac{2π}{3}\)