6.4 Amplitude and Period of Sine and Cosine Functions.

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Presentation transcript:

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 ________.

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:

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.