Section 5.4 - Section 5.4 Graphs of the Sine and Cosine...

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Unformatted text preview: Section 5.4 Graphs of the Sine and Cosine Functions Graph of Sin Look at our values for our sin function at the axis's. From this we can see what the graph should look like. Generating the graph from the circle http://www.ies.co.jp/math/java/trig/index.html Looking at this we can see the properties of the sin function 1. 2. 3. Properties of the sin function 4. 1. 2. The domain is the set of all real's The range is the set [1,1] The sin function is an odd function, which you can see by the symmetry of the graph with respect to the origin. The sin function has period 2. The x-intercepts occur at multiples of . The maximum occurs at /2+2k ... and the minimum occurs at 3/2+2k. The Graph of cos We generate the cos graph the same way as the sin. 1. 2. 3. Properties of the cos function 4. 1. 2. The domain is the set of all real's The range is the set [1,1] The cos function is an even function, which you can see by the symmetry of the graph with respect to the yaxis. The cos function has period 2. x-intercepts occurs at odd multiples of /2. The maximum occurs at 2+2k ... and the minimum occurs at +2k. Comparing sin and cos Notice that sin x = cos (x /2) Amplitude and Period Consider the following functions for >0 y=A sin(x) and y=A cos(x) Amplitude of the functions are |A|. Period of the functions , noted T, is T=2/. These come from direct consideration of the stretching properties from algebra. ...
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This note was uploaded on 08/26/2009 for the course MATH 125 taught by Professor Staff during the Fall '08 term at Southern Illinois University Edwardsville.

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