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6.3 Graphing Sine and Cosine Functions Periodic Functions • A periodic function is a function with a repeating pattern this includes sin and cos graphs. • How long does it take for the graph to repeated itself? 360 ( for degrees) OR 2 (for radians) Periodic Functions • A periodic function f exists if there is a positive constant p so: f (s+p ) = f (s) P is the period (provided it is the least possible value) y 1.0 0.8 0.6 0.4 0.2 -6 -5 -4 -3 -2 -1 1 -0.2 -0.4 -0.6 -0.8 -1.0 y = sinx 2 3 4 5 6 x Characteristics of the Sine Function 1. The domain is the set of all real numbers. 2. The range consists of all real numbers from -1 to 1, inclusive. 3. The sine function is an odd function (symmetric with respect to the origin). 4. Characteristics of the Sine Function 5. 6. Ex. • Find the value of 9pi/2 by using the graph of the sine function. • Find the values of theta for which – sin(theta) = 0 is true Graph y = sin(x) from 3pi to 5pi 1.5 (0, 1) 0 1.5 2 4 6 Characteristics of the Cosine Function 1. The domain is the set of all real numbers. 2. The range consists of all real numbers from -1 to 1, inclusive. 3. The cosine function is an even function (symmetric with respect to the y-axis). 4. 5. Characteristics of the Cosine Function 6. The graphs of the sine and cosine functions are called sinusoidal graphs. Ex: • #33 on p.364 • Graph y = cos(x) from -5pi to -3pi inclusive