### Home > APCALC > Chapter 1 > Lesson 1.3.2 > Problem1-118

1-118.

Some of the basic functions have special qualities that you have investigated in this chapter. .

1. Sketch $y = \sin(x)$ on your paper. Darken in the largest portion of the graph containing $x = 0$ for which the function passes both the horizontal and vertical line tests. State the restricted domain and range for this portion of the graph.

Graph the sin curve.

The domain is all of the $x$-values included in the graph and the range is all of the $y$-values that are included in the graph. Remember when looking at the graph that $π$ equals about $3.1415$.

2. We use the darkened portion of the graph to sketch $y = \sin^{–1}(x)$, making sure it is a function. Then state the domain and range.

Graph the inverse of $y = \sin(x)$ by reflecting the graph of $\sin(x)$ across the line $y = x$.

3. Repeat parts (a) and (b) for $y = \cos(x)$.

Repeat the steps in parts a and b using $y = \cos(x)$.

Use the eTool below to view the graphs.
Click on the link to the right to view the full version of the eTool. Calc 1-118 HW eTool