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Sum and Difference of sin/ cos graphs

Explore the graph of the function y = 3sin(2x - 1) + 4cos(2x + 3) using a graphing calculator. Determine the vital properties including the period and amplitude of the graph. Learn how to rewrite y in the form asin(b(x + c)) and understand the periodic nature of combined sine and cosine terms. Additionally, analyze related functions f(x) = sin(2x) + 4cos(3x), and f(x) = sin(½x) - 2cos(½x - 1), identifying their periods and ranges. Engage in sketched analysis to strengthen understanding.

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Sum and Difference of sin/ cos graphs

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  1. Sum and Difference of sin/cos graphs

  2. Use your graphing calculator to sketch the graph of y = 3sin(2x – 1) + 4cos(2x + 3) • What is the period of the graph? • What is the amplitude of the graph? • Rewrite y in the form asin(b(x + c)).

  3. Notice in the sum y = 3sin(2x – 1) + 4cos(2x + 3)both the sine and cosine terms have the same period. If the periods of the sine and cosine terms are different, then the combination will not be a sine (or cosine) curve, but will still be periodic.

  4. Let f(x) = sin(2x) + 4cos(3x) • Determine the period of f. • Determine the range of f.

  5. Your Turn • Let f(x) = sin( ½ x) - 2cos(½ x - 1). Rewrite f(x) in the form asin(b(x + c)). • Let g(x) = sin(3x) + 5cos(4x). • Determine the period of f. • Determine the range of f.

  6. Sketch without using a graphing calculatory = cos(2x) + sin(4x)

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