Figure 5-7b shows the graphs of y1 = cos( 60) and y2 = cos cos 60 as they might appear

Chapter 5, Problem R.2

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Figure 5-7b shows the graphs of y1 = cos( 60) and y2 = cos cos 60 as they might appear on your grapher. a. Without actually plotting the graphs, identify which is y1 and which is y Explain how you chose them. From the graphs, how can you conclude that the cosine function does not distribute over subtraction? Figure 5-7b b. Write cos ( 60) as a linear combination of sine and cosine. Verify graphically that your answer is correct. Section 5-7: Chapter Review and Test 2003 Key Curriculum Press 215 c. Write the trigonometric expression 8 cos + 15 sin as a single sinusoid with a phase displacement for y = cos x. Plot the graphs of the given expression and your answer. Explain how the two graphs confirm that your answer is correct. d. Write the circular function expression 9 cos x + 7 sin x as a single sinusoid with a phase displacement for y = cos x. Make a table of values of the given expression and your answer. Explain how the numbers in the table indicate that your answer is correct. e. Figure 5-7c shows the graphs of y1 = 4 cos x + 3 sin x and y2 = 2 as they might appear on your grapher. Solve the equation 4 cos x + 3 sin x = 2 algebraically for x [0, 2 ]. Show that the solutions agree with the graph. Figure 5-7c R