Math Help - 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.