# Trig question (sine wave)

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 :)

## Answers and Replies

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cepheid
Staff Emeritus
Gold Member
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.

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.
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.

cepheid
Staff Emeritus