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6.4

6.4. Amplitude and Period of Sine and Cosine Functions. Characteristics of the Graphs of y = sin x and y = cos x. Domain : ____________ Range : ____________ A mplitude : The amplitude of the sine and cosine functions is half the

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6.4

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  1. 6.4 Amplitude and Period of Sine and Cosine Functions

  2. Characteristics of the Graphs of y = sin x and y = cos x • Domain: ____________ • Range: ____________ • Amplitude: The amplitude of the sine and cosine functions is half the distance between the maximum and minimum values of the function. The amplitude of both y= sin x and y = cos x is ______. • Period: The length of the interval needed to complete one cycle. The period of both y= sin x and y = cos x is ________. 2

  3. Period The period of a function is the distance required to complete one full cycle. The period of the functions y = sink and y = cosk is given by:

  4. Examples: • 1.) Find the amplitude of 4cos(Θ) • 2.) Find the period of y = cos(Θ/2) and compare its graph to cos(Θ). • 3.) State the amplitude and period of y = 1/2sin(4 Θ) then graph the function. • 4.) Write an equation of the cosine function with amplitude = 9.8 and p = 6π.

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