4.4 Applications of Sinusoidal Functions and Their
Derivatives
Example 1) A power supply delivers a voltage signal according to the equation
V (t) = 20 + 12 sin ( 30 πt), where V is voltage, in volts, and t is time, in seconds.
a) Calculate the period for the voltage signal.
recall:
y = a sin k(x­c) + d
b) Calculate the frequency (in Hz) for the voltage signal.
c) Calculate the maximum and minimum signal.
d) At what times is the signal maximum?
.
Example 2) The population of a species of bird in an area can be modelled by the equation
P(t) = 450 + 200 cos (0.04πt), where P is the population and t is time, in years, after
the year 2000.
a) Determine the maximum and minimum populations, and the times at which they occur.
b) What is the period of one population cycle?
c) Determine a function that gives the rate at which the population changes
Homework:
.
page 234 example 1), p. 241 #1,2
Handout p. 325 #1ab,2a