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Graphing Sine and Cosine Help (page 3)

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By McGraw-Hill Professional
Updated on Oct 4, 2011

Examples

Sketch one period of the graph for the given function.

Table 13.3

Fig. 13.19

• y = 5 sin(3 x + π /2)
• We need to write the function in the form y = a sin k ( xb ) so that we can find k and b .

Table 13.4

Graphing Sine and Cosine Practice Problems

Practice

For Problems 1–3, match the function with its graph shown in Figures 13.21–13.23. The dashed graph is the graph of one period of y = cos x . The solid graph is the graph of one period of a transformation.

Fig. 13.20

Fg. 13.21

Fig 13.22

Fig. 13.23

1. y = 2 cos( x − π /3)
2. y = 3 cos ( x + π /2)
3. y = cos( x − π )
4. Find the amplitude, period, and phase shift for .
5. Find the amplitude, period, and phase shift for y = 6 sin(2 xπ /2).
6. Sketch one period for the graph of .
7. Sketch one period for the graph of y = − 1 + 2 sin( xπ /3)

Solutions

1. Figure 13.22
2. Figure 13.21
3. Figure 13.23
4. The amplitude is | −3 | = 3, the period is , and the phase shift is b = π /4.
5. In order to find k and b , we need to write the function in the form y = a sin k ( xb ).

The function can be written as y = 6 sin 2( x − π /4). Now we can see that the amplitude is |6| = 6, the period is 2 π /2 = π , and the phase shift is π /4.

1. Plot points for x = − π /4, 3 π /4, 7 π /4, 11 π /4, and 15 π /4.

Fig. 13.24

2. Plot points for x = π /3, 5 π /6, 4 π /3, 11 π /6, and 7 π /3.

Fig. 13.25

Practice problems for this concept can be found at: Trigonometry Practice Test.

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