Download Lesson 6 – Applications

MHF4U
Trig Function Applications
Trig applications can be used to model many real world phenomena, especially relating cyclical
trends (weather, tides, springs, etc.)
Before, when graphing trig functions, we scaled the 𝑥-axis in terms of radians. Now we will use
horizontal stretches or compressions to alter the period to fit the situation.
Example 1
The water depth in a harbour is 8 𝑚 at low tide and 20 𝑚 at high tide. One cycle
is completed every 12 hour.
a) Graph the water depth for 24 hours starting at high tide.
b) Find the equation.
c) Find the water depth at 5 hours.
Example 2 A Ferris wheel with a radius of 9.5 𝑚 rotates every 10 𝑠. The bottom of the
wheel is 1.2 𝑚 above the ground.
a) Graph the rider’s height above ground as a function of time when the rider boards the
ride at the bottom. Graph for 2 cycles.
b) Find the equation.
c) Find the height of a rider 3 seconds into the ride.
d) When is a person at a height of above 10 𝑚 in the first rotation?
Example 3
The frequency of a periodic function is defined as the number of cycles
completed in 1 𝑠 and is typically measured in Hertz (𝐻𝑧). It is the reciprocal of
the period of a periodic function.
a) One of the A-notes from a flute vibrates 440 times in 1 𝑠. It is said to have a frequency
of 440 𝐻𝑧. What is the period of the A-note?
b) The sound can be modelled using a sine function of the form 𝑦 = sin 𝑘𝑥. What is the
value of 𝑘?
Example 4
a)
b)
c)
d)
The voltage of the electricity supply in North America can be modelled using a
sine function. The maximum value be modelled using a sine function. The
maximum value of the voltage is about 120 𝑉. The frequency is 60 𝐻𝑧.
What is the amplitude of the model? Assume the equation is of the form𝑦 = 𝑎 sin 𝑘𝑥.
What is the period of the model?
Determine the equation of the model.
Graph the model over two cycles.