Thread: 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.

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:

or


Please use parenthesis!

-Dan

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.

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 is obviously meant to be in the argument of the sine function; I will take the 200 as outside.


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 . So find when is :


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

Thank you, Dan!!!