Section 4.4 Graphs of Sine and Cosine.pdf

Section 4.4 Graphs of Sine and Cosine.pdf - 4.4 Graphs of...

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4.4 Graphs of the Sine and Cosine Functions A. Basic Graphs of Sine and Cosine Def . A function 𝑓(?) is said to be periodic if there is a positive number p, such that 𝑓(? + 𝑝) = 𝑓(?) In other words, the function will repeat itself over an interval of length p. Sine is Periodic: sin(? + 2𝜋) = sin ? Cosine is Periodic: cos(? + 2𝜋) = cos ?.

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II. Amplitude and Period: ? = ? 𝐬𝐢? ?? and ? = ? 𝐜?𝐬 ?? |?| is called the amplitude . The amplitude changes the range of the graph to [−?, ?]. If ? > 0 and a whole number, we stretch the graph vertically. If 0 < ? < 1 , we shrink the graph vertically. If ? < 0, reflect the graph over the x-axis. b affects the period of the graph by compressing it or stretching it

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