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18434672-Gr12-Advance-Function-Ch51 - 5.1 Graphs of Sine...

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Graphs of Sine, Cosine, and Tangent Functions 5.1 Investigate How can you use graphs to represent trigonometric functions? 1. a) Copy and complete the table. Use your knowledge of special angles to determine exact values for each trigonometric ratio. Then, use a scientific calculator set to Radian mode to determine approximate values, to two decimal places. One row has been completed for you. b) Extend the table to include multiples of the special angles in the other three quadrants. Tools • scientific calculator • grid paper Optional • graphing calculator OR • graphing software Trigonometric ratios are typically first introduced using right triangles. Trigonometric ratios can be extended to define trigonometric functions, which can be applied to model real-world processes that are far removed from right triangles. One example is the business cycle, which models the periodic expansion and contraction of the economy. Time Business Cycle Economy Angle, x y sin x y cos x y tan x 0 π _ 6 1 _ 2 0.50 3 _ 2 0.87 1 _ 3 0.58 π _ 4 π _ 3 π _ 2 252 MHR • Advanced Functions • Chapter 5

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2. a) Graph y sin x on the interval x [0, 2 π ]. b) Create a table to summarize the following characteristics of the function y sin x . Include two additional columns, one for y cos x and the other for y tan x , to be filled in later. • the maximum value, the minimum value, and the amplitude • the period, in radian measure • the zeros in the interval x [0, 2 π ] • the y -intercept • the domain and range 3. a) Graph y cos x on the interval x [0, 2 π ]. b) Determine the following characteristics of the function y cos x . Add the results to your table from step 2b). • the maximum value, the minimum value, and the amplitude • the period, in radian measure • the zeros in the interval x [0, 2 π ] • the y -intercept • the domain and range 4. Reflect a) Suppose that you extended the graph of y sin x to the right of 2 π . Predict the shape of the graph. Use a calculator to investigate a few points to the right of 2 π . At what value of x will the next cycle end? b) Suppose that you extended the graph of y sin x to the left of 0. Predict the shape of the graph. Use a calculator to investigate a few points to the left of 0. At what value of x will the next cycle end? 5. Reflect Repeat step 4 for y cos x . 6. a) Inspect the column for y tan x in your table from step 1. Why are some values undefined? b) Use a calculator to investigate what happens to tan x as x π _ 2 . Then, investigate what happens to the value of tan x as x π _ 2 . Report your findings, and explain why this happens. 7. a) Graph y tan x on the interval x [0, 2 π ]. Use your results from step 6 to determine how the graph should be drawn close to x π _ 2 and x 3 π _ 2 . Sketch vertical dotted lines at these locations. What name is given to these lines?
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18434672-Gr12-Advance-Function-Ch51 - 5.1 Graphs of Sine...

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