Trig question (sine wave)

1. Jun 2, 2009

Imperil

A piston in a large factory engine moves up and down in a cylinder. The height, h centimeters, of the piston at t seconds is given by the formula h = 120sinPi(t)+200.

a) State the amplitude and period.
b) What are the maximum and minimum heights of the piston?
c) How many complete cycles does the piston make in 30 min?

ai) amplitude = 120cm
aii) period = 2Pi / Pi = 2

bi) minimum height = 200cm - 120cm = 80cm
bii) maximum height = 200cm + 120cm = 320cm

c) 30m = 1800s
period = 2 cycles / s
1800 x 2 = 3600

Therefore the piston makes 3600 complete cycles in 30 minutes.

I was hoping that someone could tell me if my answers are correct? I want to make sure that I understand this properly. Thanks :)

2. Jun 2, 2009

cepheid

Staff Emeritus
Part c looks wrong. The period is 2 seconds, which corresponds to half a cycle per second. You know that if it takes *longer* than one second to go through a complete cycle, then you will able to go through *fewer* than 1800 full cycles in 1800 seconds.

3. Jun 2, 2009

Imperil

Oops sorry about that I typed it in wrong :(

I meant the following:

c) 30m = 1800s
period = 2
1800s / 2 = 900

Therefore the piston makes 900 complete cycles in 30 minutes. Thanks for pointing that out.

4. Jun 2, 2009

cepheid

Staff Emeritus
No problem. Everything else looks good to me.