1. 6.3 Graphing Sine and Cosine Functions

2. 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)

3. 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)

4. y = sinx

5. 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.

6. Characteristics of the Sine Function 5. 6.

7. 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

8. (0, 1)

9. 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.

10. Characteristics of the Cosine Function 6.

11. The graphs of the sine and cosine functions are called sinusoidal graphs.

12. Ex: #33 on p.364 Graph y = cos(x) from -5pi to -3pi inclusive