1. Chapter 6 Section 6.3 Graphs of Sine and Cosine Functions

2. Trigonometric Graphs The graphs of trigonometric functions are usually represent on a xy -coordinate system. The x -axis runs horizontally and the y -axis runs vertically. The values for x usually represent radians. This is because if degrees were used the graphs themselves would look greatly distorted if you do not adjust the scaling. Periodic Functions Since all the trigonometric functions are combinations of the x and y coordinates of points on the unit circle they will repeat every time you go around the unit circle. sin( x ) =sin( x +2  ) andcos( x ) =cos( x +2  ) This enables you to find the graph of sin x and the cos x between 0 and 2  then just repeat the same pattern in the graph. x Terminal Pointsin x cos x 0(1,0)01  /2 (0,1)10  (-1,0)0 3  /2 (0,-1)0 22 (1,0)01

3. Both of the graphs above show one wave (period) of the functions y = sin x and y = cos x. If the graph continued it would look as shown. 0++++++++++++0-------------------0 ++++++0-------------------0++++++

4. Amplitude How high above and below the centerline a wave (period) goes is called the amplitude. Putting a number (other than 1) in front of the sine and cosine will change its amplitude by that number. A negative number in front flips it around the x -axis.

5. Solve for the values of x : The graph is a sine wave flipped about x -axis.

6. Find the equation of the trigonometric functions graphed below.