5.3 Investigate the Sine Function
Prerequisite Skills
1. a) Plot the ordered pairs (0, 2), (0,0),(-1,0), (2, -2), (1,0), and (-2, -2).
b) Describe the pattern made by the points.
2. Write the meaning of each statement.
1. a) Make a table of values for y = sin x, using x = 0°, 30°, 60°, ..., 360°. Round the y-values to four decimal places.
b) Extend the table to 720°. What do you notice?
c) Use your table to draw a sketch of y = sin x. Label all intercepts and all maximum and minimum points.
2. A monorail operates at an amusement park to transport guests from one side of the park to the other. The monorail travels on a circular track around the perimeter of the park. The park has a radius of 3 km. One station is located at the easternmost point of the park.
a) Draw the train track and station and collect data representing the distance of the monorail train north or south of the station, relative to the angle of rotation.
b) Use your data to sketch a graph of the angle versus distance north or south of the station for one revolution around the track
c) How does the graph compare to that of y = sin x?
3. A jack-in-the-box has a crank handle with a length of 1 dm (10 cm), and is rotated counterclockwise from a horizontal position.
Draw a diagram
a) What is the height of the handle, in decimetres, relative to its centre of rotation after it rotates 50%?
b) What is the height of the handle, in decimetres, relative to its centre of rotation after it rotates 210%?
c) How many degrees has the handle rotated through when its height is 0.9 dm relative to its centre of rotation?
4. a) Find an equation of the line that passes through all the minimum points of y = sin x.
b) Find an equation of the line that passes through the points on - sin x where x = 90° and x = 180°.
5. a) Sketch the graph of y = cos x on the same axes as y = sin x.
b) How can you verify that y = cos x is a function?
c) Compare the graphs of y = sin x and y = cos x. How are they the same? How are they different?
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