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6.4 – Amplitude and Period of Sine and Cosine Functions Let’s review How would the graph of g(x) = 3x2 compare to the parent graph of f(x) = x2 Amplitude The similar effect will happen for sine and cosine functions. Not only to they stretch the graphs, it changes the maximum values. The maximum value of y = Asinθ or y = Acosθ is equal to |A| The absolute value of A is called the amplitude Amplitude It can also be described as the absolute value of half the difference of the maximum and minimum values of the function. Example: y = 4sinθ The amplitude is 4… The maximum is 4 and the minimum is -4. So (4 - -4)/2 = 4 y = -2cosθ State the amplitude b) Graph the function and y = cosθ on the same set of axes. c) Compare the graphs. a) In your calculator, graph the following functions in the same window y = sinθ 2. y = sin(4θ) 3. y = sin(θ/4) 1. Compare the three graphs Period The period of the functions y = sin(kθ) and y = cos(kθ) is 2π/k, where k > 0 State the period of the functions. 1. y = cos(θ/3) 2. y = sin(6θ) Write an equation of the cos function given the amplitude and period 1. amplitude: 17.9; period: π/7 2. Amplitude: 5/3; period: 30