How to Graph Inverse of the Cosine Function?
Inverse cosine returns an angle from zero to pi for inputs from negative one to one. Its graph reverses the restricted cosine function.
The inverse of cosine is one of the inverse trigonometric functions. In this guide, you will learn more about the inverse of the cosine function and graph it.
Graph Inverse of the Cosine Function: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Choose the modelUse a right triangle, the unit circle, or a transformed graph.
- Track unitsConvert degrees and radians when needed.
- Use identitiesReplace complicated trig expressions with equivalent simpler ones.
Worked examples
Read arcsine
- Arcsine reverses the restricted sine graph.
- The input must be a sine output, so x is between -1 and 1.
- The principal outputs run from -pi/2 to pi/2.
Read arctangent
- Arctangent's outputs approach pi/2 and -pi/2.
- Those are y-values, so they are horizontal asymptotes.
- The graph never reaches them.
Try one before moving on
Graph Inverse of the Cosine Function: pop-up practice
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 \(y=cos\:x\:⇒\:x=cos^{-1}\left(y\right)\)
Type the problems from this lesson and check each step.
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 \(x = -\frac{1}{2}\rightarrow y = \frac{2π}{3}\)
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