# Need Help with Trig Modeling

• Mar 19th 2009, 05:52 PM
tictac
Need Help with Trig Modeling
Could someone help me with trig modeling problem?

4)Assume that are aboard a submarine, submerged in the Pacific Ocean. At time t=0 you make contact with an enemy destroyer. Immediately, you start "porpoising" ( going deeper and shallower). At time t= 4 minutes, you are at your deepest, y= -1000 meters. At time t= 9 minutes, you next reach your shallowest, y= -200 meters. Assume that y vries sinusoidally with t for t > 0.
a) Sketch the graph of y versus t.

b) Write the particular equation expressing y in terms of t.

c) Your submarine is "safe" when it is below y = -300 meters. At time t=0, was your submarine safee? Justify your answer.
• Mar 19th 2009, 11:20 PM
Trig equation
Hello tictac
Quote:

Originally Posted by tictac
Could someone help me with trig modeling problem?

Quote:

Originally Posted by tictac
4)Assume that are aboard a submarine, submerged in the Pacific Ocean. At time t=0 you make contact with an enemy destroyer. Immediately, you start "porpoising" ( going deeper and shallower). At time t= 4 minutes, you are at your deepest, y= -1000 meters. At time t= 9 minutes, you next reach your shallowest, y= -200 meters. Assume that y vries sinusoidally with t for t > 0.
a) Sketch the graph of y versus t.

b) Write the particular equation expressing y in terms of t.

c) Your submarine is "safe" when it is below y = -300 meters. At time t=0, was your submarine safee? Justify your answer.

The equation you need will be something like

$\displaystyle y = a\sin b(t+c) +d$

In this equation, the amplitude = $\displaystyle a$ = half the difference between the deepest and shallowest positions. (So you can work out the value of $\displaystyle a$, from the information given.)

The period $\displaystyle = \frac{2\pi}{b}=$ the time for one complete 'cycle' = twice the time between the deepest and shallowest positions. (So you can work out the value of $\displaystyle b$.)

$\displaystyle d$ represents the average depth; so it's mid-way between the deepest and shallowest. $\displaystyle y$ then varies from $\displaystyle d+a$ to $\displaystyle d-a$.

$\displaystyle c$ is the phase shift; you can work it out (once you've found $\displaystyle a, b$ and $\displaystyle d$) if you know a value of $\displaystyle y$ at a certain time t. So plug $\displaystyle t = 4, y = -1000$ into your equation, and you're there.

• Mar 20th 2009, 06:28 AM
tictac
Need help with Trig Modeling
y = -400 sin (.628t -.943) - 600.

Quote:

Hello tictacThe equation you need will be something like

$\displaystyle y = a\sin b(t+c) +d$

In this equation, the amplitude = $\displaystyle a$ = half the difference between the deepest and shallowest positions. (So you can work out the value of $\displaystyle a$, from the information given.)
The period $\displaystyle = \frac{2\pi}{b}=$ the time for one complete 'cycle' = twice the time between the deepest and shallowest positions. (So you can work out the value of $\displaystyle b$.)
$\displaystyle d$ represents the average depth; so it's mid-way between the deepest and shallowest. $\displaystyle y$ then varies from $\displaystyle d+a$ to $\displaystyle d-a$.
$\displaystyle c$ is the phase shift; you can work it out (once you've found $\displaystyle a, b$ and $\displaystyle d$) if you know a value of $\displaystyle y$ at a certain time t. So plug $\displaystyle t = 4, y = -1000$ into your equation, and you're there.