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Consider the function .

  1. Make a complete graph of the function.

  2. Write a simpler trigonometric function that is represented by the same graph.

    Which trig function passes through the origin?

  3. Now use the angle sum identity to expand and simplify .

    Review the Math Notes box in this lesson and problem 12-108 for the Angle Sum Identities.

  4. Does your work in part (c) agree with your graphical results from parts (a) and (b)? Explain.

    Your answers should agree.