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.

Need help with Trig Modeling

Thanks Grandad! I already solved it! The ans I got is:

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

Quote:

Originally Posted by

**Grandad** Hello tictacThe equation you need will be something like

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

Thanks Grandad! I already solved it! The ans I got is:

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

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.

Grandad