# Thread: Need Help with Trig Modeling

1. ## 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.

2. ## Trig equation

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

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

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

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

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

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

3. ## Need help with Trig Modeling

y = -400 sin (.628t -.943) - 600.

Hello tictacThe equation you need will be something like

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

y = -400 sin (.628t -.943) - 600.

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

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

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

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