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.
\[11. y=3\sin (8(x+4))+5\] \[12. y=4\sin \left(\frac{\pi }{2} (x3)\right)+713. y=2\sin (3x21)+4\]
\[14. y=5\sin (5x+20)2\]
\[15. y=\sin \left(\frac{\pi }{6} x+\pi \right)3\]
\[16. y=8\sin \left(\frac{7\pi }{6} x+\frac{7\pi }{2} \right)+6\]
Find a formula for each of the functions graphed below.
17.
18.
19.
20.

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.

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.

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.

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

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

How high are you off the ground after 5 minutes?

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.

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

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

How high are you off the ground after 4 minutes?
Section 6.2 Graphs of the Other Trig Functions 415