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.

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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 = sinx

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

(0, 1)

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)

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