Applications of trig graphs Graphs and equations.

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Presentation transcript:

Applications of trig graphs Graphs and equations

Ferris Wheel This trig graph represents the height above the ground of a seat on a Ferris Wheel as the Ferris wheel rotates about its hub. 1.What is the period of this trig graph? 2.What does the period represent in this situation? 3.What is the height above the ground of the hub of the Ferris wheel? 4.What is the amplitude of this trig graph? 5.A ‘ride’ on this Ferris wheel is 5 revolutions. How long does a ride last? 6.The first time the seat is 10m above the ground is at 10 seconds. When is the second time? 7.When is the seat 15m above the ground for the first time?

Tuning Forks Sounds are modelled by trig graphs. The intensity of loudness of the sound is measured in decibels. The pitch is related to the frequency of the vibrations. This is measured in hertz. Hertz is the number of cycles per second. This graph shows two complete cycles of sound produced by the tuning fork. 1.What is the time for one complete cycle? 2.What is the period of this trig graph? 3.What is the amplitude of this trig graph? 4.What is the frequency in hertz of the sound produced?

The simple sine curve y=sin(x)

Amplitude increase y=3sin(x)

Increased Frequency y=sin(3x)

Vertical Shift y=sin(x)+3

Horizontal Shift y=sin(x-60)

Another Ferris wheeeel On this Ferris wheel the lowest point is 1m above the ground. The HUB of this wheel is 15m above the ground. One complete revolution takes 1 minute (60 seconds). The height of one seat which starts at 1m can be modelled by a cosine function of the form: (t is time measured in seconds) Sketch a graph to model the situation. What will be the maximum height of the seat? Find A, B and C. y = A cos (Bt) + C Michelle feels queasy when she is over 20 m above the ground. For how long each revolution will she feel ill?

Body Chemicals The level of a certain hormone in the blood is cyclical over a period of 60 days. The maximum quantity is 600 µL and the minimum is 280 µL. It can be modelled by the equation : Q = A Cos (Bt) + C Sketch the graph to model this situation and hence find the values of A, B and C. When the hormone level is below 350 µL it can be a critical time for males with a certain condition. For how long each cycle can a man with this condition be in a critical state?

Merit Modelling The level of a certain hormone in the blood is cyclical over a period of 40 days. The maximum quantity is 60µL and the minimum is 14µL. Use a trig function to model the level of hormone in the blood between successive peaks. Do a quick graph sketch. Put numbers on the axes using the information given. Use this sketch to help you with your model.