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Mathematics LibreTexts

6.1E: Sinusoidal Graphs (Exercises)

  • Page ID
    13923
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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. image 6. image

    7. image 8. image

    9. image 10.image

    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. image

    18. image

    19. image

    20. image

    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