5.1 Periodic Functions

Prerequisite Skills

1. Evaluate each expression for the value indicated. Round to four decimal places. 

a) -2 sin θ, for θ= 60°

b) ½ tan(2θ + 30°), for θ= 45°

2. a) Plot the ordered pairs (0, 2), (-1, -1), (-1, 1), (0, -2), (1, -1), and (1, 1).

b) Describe the pattern made by the points.

5. The table shows the mean monthly amounts of precipitation for Mount Forest, ON, using recorded data from over 100 years.

a) Make a scatter plot of the data and draw a curve of best fit.

b) Does this data represent a periodic function? Explain your reasoning.

c) What are the maximum and minimum amounts of precipitation for Mount Forest? When do they occur?

6. The graph shows the mean monthly high and low temperatures, in degrees Celsius, for Windsor, ON, using recorded data from 50 years.

7. The table shows the distance, in centimetres, from the number 12 on an analog clock to the tip of the second hand.

a) Assume that the data are periodic. Make a scatter plot of the data and extend it to 60 s.

b) How does the graph show that the data are periodic? Determine the period and amplitude of the function.

8. Carlos is cycling at a constant speed. The bicycle pedals have a maximum height of 35 cm and a minimum height of 5 cm from the ground. Carlos makes one revolutions in 0.8 s. Sketch a graph representing a pedal's height above the ground, relative to time, for a 3-s period starting with the pedal at the minimum height.