# Thread: trig word problem; sinusoidal function

1. ## trig word problem; sinusoidal function

A piston in an engine moves up and down in a cylinder. The height, h centimetres, of the piston a t seconds is given by the formula h= 120 sin Pi t+ 200.
-State amplitude & period
-State max & min. heights of piston
-How many complete cycles does the piston make in 30 min.

I have no idea where to start. Is this the same as y=a sin k(x+c)? Should I graph the equation as is and go from there?

Thanks in advance for any suggestions!

W.

2. Originally Posted by sux@math
A piston in an engine moves up and down in a cylinder. The height, h centimetres, of the piston a t seconds is given by the formula h= 120 sin Pi t+ 200.
-State amplitude & period
-State max & min. heights of piston
-How many complete cycles does the piston make in 30 min.

I have no idea where to start. Is this the same as y=a sin k(x+c)? Should I graph the equation as is and go from there?

Thanks in advance for any suggestions!

W.
Well for starters is this equation:
$h = 120 ~ sin(\pi t) + 200$
or
$h = 120 ~ sin(\pi t + 200)$

-Dan

3. Thanks for the quick reply! Um . . . I'm sorry, but the equation in my book has no parentheses! (it's kind of a crap correspondence course I am taking for Grade 11 Math)....

It reads exactly how I typed it in my first post.

4. Originally Posted by sux@math
A piston in an engine moves up and down in a cylinder. The height, h centimetres, of the piston a t seconds is given by the formula h= 120 sin Pi t+ 200.
-State amplitude & period
-State max & min. heights of piston
-How many complete cycles does the piston make in 30 min.
All right then, we read it almost without any parenthesis. The $\pi t$ is obviously meant to be in the argument of the sine function; I will take the 200 as outside.
$h = 120 ~sin(\pi t) + 200$

The amplitude should be obvious, its 120 cm.

The period of a function is how much time it takes for one oscillation. One oscillation of the sine function is $2\pi$. So find when $\pi t$ is $2 \pi$:
$\pi T = 2 \pi \implies T = 2~s$

I'll leave it to you to determine the max and min heights.

As to how many complete cycles are in a time period of 30 minutes, how many periods are in 30 minutes? (Remember that the period is in seconds, not minutes!)

-Dan

5. Thank you, Dan!!!