Harvard University Math Trigonometry Geometry Worksheet

Description

2 attachmentsSlide 1 of 2attachment_1attachment_1attachment_2attachment_2

Unformatted Attachment Preview

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

Purchase answer to see full
attachment

Explanation & Answer:
10 Pages

Tags:
math

geometry

trigonometry

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.

Peter M.
Peter M.
So far so good! It's safe and legit. My paper was finished on time...very excited!
Sean O.N.
Sean O.N.
Experience was easy, prompt and timely. Awesome first experience with a site like this. Worked out well.Thank you.
Angela M.J.
Angela M.J.
Good easy. I like the bidding because you can choose the writer and read reviews from other students
Lee Y.
Lee Y.
My writer had to change some ideas that she misunderstood. She was really nice and kind.
Kelvin J.
Kelvin J.
I have used other writing websites and this by far as been way better thus far! =)
Antony B.
Antony B.
I received an, "A". Definitely will reach out to her again and I highly recommend her. Thank you very much.
Khadija P.
Khadija P.
I have been searching for a custom book report help services for a while, and finally, I found the best of the best.
Regina Smith
Regina Smith
So amazed at how quickly they did my work!! very happy♥.