The inverse cosine function, denoted as $y = \arccos(x)$ or $y = \cos^{-1}(x)$, gives the angle whose cosine is $x$. Remember, the domain of $\arccos(x)$ is $[-1, 1]$, and the range is $[0, \pi]$. Graphing inverse cosine involves reflecting the restricted cosine function (on the interval $[0, \pi]$) over the line $y = x$. This worksheet provides practice to solidify your understanding of graphing these functions.
Understanding the transformations of inverse cosine graphs is crucial. These transformations include vertical and horizontal shifts, stretches, and reflections. Recognizing how these changes affect the parent function $y = \arccos(x)$ will enable you to accurately sketch various inverse cosine graphs.
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Inverse Cosine | A. The range of $\arccos(x)$. |
| 2. Domain | B. The input values of a function. |
| 3. Range | C. The function that returns the angle whose cosine is a given number. |
| 4. Amplitude | D. The output values of a function. |
| 5. $[0, \pi]$ | E. Half the distance between the maximum and minimum values of a trigonometric function. |
Complete the following paragraph with the correct words:
The inverse cosine function, also known as __________, is the inverse of the __________ function. Its domain is __________ and its range is __________. The graph of $y = \arccos(x)$ is a reflection of the restricted cosine function across the line __________.
Explain how changing the equation $y = \arccos(x)$ to $y = 2\arccos(x-1)$ affects the graph. Be specific about the transformations involved.
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