1. Trigonometric Graphing Day 1 What do the graphs look like?

2. Sin x 1 x y Lets plot some points 0 Now connect the dots Graph does continue Amplitude = 1

3. Cos x 1 x y Lets plot some points 0 Now connect the dots Graph does continue Amplitude = 1

4. Tan x 1 x y Lets plot some points 0 Now connect the dots Graph does continue Asymptote

5. Shifts Sin x 1 Flips Graph Shifts up/down Shifts left/right 2 Inc or Dec Amplitude Inc or Dec Period

6. Basic Truths The period (that is, cycle length) of both y = sin x and y = cos x is 2π. The amplitude of both functions is 1. For a standard, we start both of these functions at x = 0 and finish at x = 2π.

7. So what trends do we observe? Add outside? Move graph  Add inside? Moves graph  Multiply outside? Changes Amplitude Multiply inside? Changes Period 

8. Do I have to memorize these? Well, to a degree you should know what to expect. Some teachers want you to look at the graph, determine where it will start and end, determine what the amplitude is, then just graph. I will teach you a mathematical method that you can memorize.

9. Equation Change Amplitude Changes Period Moves left or Right Moves up or down Can substitute any Trig Function

10. My Method 1.Determine New Start: Set Argument = 0 2.Determine New End: Set Argument = 2π (or New Start + Period) 3. Find 3 midpoints 4. Plot these 5 points

11. Now lets Graph it! 1 4 -2 Amp= 3

12. Now lets Graph it! 1