
# 6.1E: Sinusoidal Graphs (Exercises)

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Section 6.1 Exercises

1. Sketch a graph of $$f\left(x\right)=-3\sin \left(x\right)$$.

2. Sketch a graph of $$f\left(x\right)=4\sin \left(x\right)$$.

3. Sketch a graph of $$f\left(x\right)=2\cos \left(x\right)$$.

4.  Sketch a graph of $$f\left(x\right)=-4\cos \left(x\right)$$.

For the graphs below, determine the amplitude, midline, and period, then find a formula for the function.

5. 6.

7. 8.

9. 10.

For each of the following equations, find the amplitude, period, horizontal shift, and midline.

$11. y=3\sin (8(x+4))+5$ $12. y=4\sin \left(\frac{\pi }{2} (x-3)\right)+713. y=2\sin (3x-21)+4$

$14. y=5\sin (5x+20)-2$

$15. y=\sin \left(\frac{\pi }{6} x+\pi \right)-3$

$16. y=8\sin \left(\frac{7\pi }{6} x+\frac{7\pi }{2} \right)+6$

Find a formula for each of the functions graphed below.

17.

18.

19.

20.

1. Outside temperature over the course of a day can be modeled as a sinusoidal function. Suppose you know the temperature is 50 degrees at midnight and the high and low temperature during the day are 57 and 43 degrees, respectively. Assuming t is the number of hours since midnight, find a function for the temperature, D, in terms of t.

1. Outside temperature over the course of a day can be modeled as a sinusoidal function. Suppose you know the temperature is 68 degrees at midnight and the high and low temperature during the day are 80 and 56 degrees, respectively. Assuming t is the number of hours since midnight, find a function for the temperature, D, in terms of t.

1. A Ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function $$h(t)$$ gives your height in meters above the ground t minutes after the wheel begins to turn.

2. Find the amplitude, midline, and period of $$h\left(t\right)$$.

3. Find a formula for the height function $$h\left(t\right)$$.

4. How high are you off the ground after 5 minutes?

1. A Ferris wheel is 35 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function $$h(t)$$ gives your height in meters above the ground t minutes after the wheel begins to turn.

2. Find the amplitude, midline, and period of $$h\left(t\right)$$.

3. Find a formula for the height function $$h\left(t\right)$$.

4. How high are you off the ground after 4 minutes?

Section 6.2 Graphs of the Other Trig Functions 415