4.1.1: Graphs of the Sine and Cosine Functions (Exercises)

Activity 3.1

Graph of the Sine and Cosine Functions

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I. For the following exercises, graph the functions for two periods and determine the amplitude or stretching factor, period, midline equation, and asymptotes.

1. \(f(x)=-3 \cos x+3\)

2. \(f(x)=\frac{1}{4} \sin x\)

3. \(f(x)=3 \cos \left(x+\frac{\pi}{6}\right)\)

4. \(f(x)=-2 \sin \left(x-\frac{2 \pi}{3}\right)\)

5. \(f(x)=3 \sin \left(x-\frac{\pi}{4}\right)-4\)

6. \(f(x)=2\left(\cos \left(x-\frac{4 \pi}{3}\right)+1\right)\)

7. \(f(x)=6 \sin \left(3 x-\frac{\pi}{6}\right)-1\)

8. \(f(x)=-100 \sin (50 x-20)\)

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