Chapter 7: Q. 6 (page 505)

Use transformations to graph the equation $y = \cos (x - \frac{π}{2}) - 1$ .

Short Answer

Expert verified

The graph is

Step by step solution

Step 1. Given Information

We are given the equation $y = \cos (x - \frac{π}{2}) - 1$ and we need to use transformations to graph it.

Step 2. Using transformations

From the concept of the vertical and horizontal shift we know, the graph of $g (x) = f (x + c) + k$ will be the graph of $f (x)$ shifted left or right by $c$ units depending upon the sign and up or down by $k$ units depending upon the sign.

The equation can be written as:

$y = \cos (x - \frac{π}{2}) - 1 \Rightarrow y + 1 = \cos (x - \frac{π}{2})$

Let $X \equiv x - \frac{π}{2} Y \equiv y + 1$

The lines pass through $X = 0, Y = 0$ .

$∴ x - \frac{π}{2} = 0 \Rightarrow x = \frac{π}{2} y + 1 = 0 \Rightarrow y = - 1$

Step 3. Plotting the graph

The graph of the equation is

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Use transformations to graph the equation $y = \cos (x - \frac{π}{2}) - 1$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Using transformations

Step 3. Plotting the graph

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Use transformations to graph the equationy=cosx-π2-1.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Using transformations

Step 3. Plotting the graph

One App. One Place for Learning.

Most popular questions from this chapter

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Use transformations to graph the equation $y = \cos (x - \frac{π}{2}) - 1$ .