Graphing Trigonometric Functions

1. Graphing Trigonometric Functions

2. Phase shift: C>0 left C<0 right Period = 2π/B Vertical shift: middle of graph Amplitude Standard Form y = D + A sin (B(x + C)) Please note that this is slightly different than the standard form given in the book.

3. This presentation will give you the general steps for graphing sin and cos functions. We will also go through a specific example as we cover the general steps. Here is our example:

4. Step 1: Get the equation in standard form: y = D + Asin(B(x+C)) This may involve factoring out the B value.

5. Step 2: Use D to find the middle of the graph (draw a dashed reference line lightly on your graph). D moves the graph up and down. D = 3

6. Step 3: Use A to find the max and min of the graph. A is the amplitude = the distance between the middle and the max. A = 4 Therefore: max = 3 + 4 = 7 min = 3 - 4 = -1

7. Step 4: Determine the labels for the x-axis. Each mark should be 1/4 of the period apart. This is the space between “special points” (max, min, and middle) on the x-axis – it is 1/4 of the period = 2π/B. B = 2 space between special points = π/4

8. Step 5: Find the “starting point” of the graph. • C shifts the graph left and right: C>0 shift left, C<0 shift right • sin starts in the middle, + cos starts at the max, - cos starts at the min “Starting point” is at the middle, π/4 to the left.

9. Step 6: Put in at least 2 cycles worth of “special points.” Keep in mind that for a sin graph you start in the middle and go up to the right if it is a +sin and down to the right if it is a -sin. +sin, so go up to the right.

10. Step 7: “Connect the dots.” Make sure to draw nice rounded corners!

11. Remember: A changes the Amplitude.

12. B changes the period: Period = 2π/B

13. D changes the middle.

14. C moves the graph left and right – also called the “phase shift”.