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MTH 112 FWH 6 – Modeling with Trigonometric Functions

1. The outside temperature over the course of a day can be modeled as a sinusoidal function.

Suppose you know the temperature varies sinusoidally between 52 and 76 degrees throughout

the 24 hour day with the average temperature occurring at midnight. Determine a function

modeling the temperature throughout the day and then determine which hours of the day the

temperature is above 70 degrees.

2. Suppose the high tide in Seattle occurs at 1:00 am and again at 1:00 pm at which times the

water is 10 feet above the height of low tide. Low tide occurs 6 hours after the high tides.

Supposing there are two high tides and two low tides every day and the height of the tide

varies sinusoidally, find a formula for the function y = h(t) that computes the height of the

tide above low tide at time t. (So y=0 corresponds to low tide). Then determine the tide

height at 11:30am. Finally, determine the hours of the day when the tide is less than or equal

to 3 feet above low tide.

1

3. Find a function of the form y = a sin

π

x + m + bx that fits the data:

2

4. Find a function of the form y = abx cos

x

y

0

1

1

2

2

9

3

16

x

y

0

3

1

5

2

47

9

3

5

π

x + c that fits the data:

2

5. A spring is attached to the ceiling and pulled 19 cm down from equilibrium and released.

After 4 seconds the amplitude has decreased to 14 cm. The spring oscillates 13 times each

second. Assuming exponential amplitude decay, determine a function which models the

distance, D, the end of the spring is below equilibrium in terms of seconds, t, since the spring

was released. Hint: To find the factor of exponential decay, note that the initial amplitude is

19 and then look at A(t) = A0 · bt is the amplitude function and plug in (4,14) into this to

solve for b.

2

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Explanation & Answer:

10 Pages

Tags:

math

geometry

trigonometry

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