Advanced Algebra Trig. Name ______

Notes-Graphing Trig. Transformations

To graph trig. equations that include transformations, you will need to memorize the 5 points for each of the 6 trig. parent functions and be able to sketch them easily.

We will graph the trig. functions using a 5-step approach. Each of the 5 steps represents a transformation from the original parent graph.

Steps to graphing trig. functions of the form:

1. Parent-Make a chart including the 5 points for that trig. function.

2. Period- In a separate chart, take each ‘x’ value from step 1 and divide it by the ‘B’ value and record under the x-column.

3. Amplitude- Take each ‘y’ value from step 1 and multiply it by the ‘A’ value. (y*a) and record under the y-column.

4. Phase Shift- In a separate chart, take the ‘x’ value from step 2 and add and record under the x-column.

5. Vertical Shift- Take the ‘y’ value from step 3 and add ‘D’ value. Record under the y-column. These points comprise the final graph and should be drawn and scaled on graph paper.

You might find it helpful for a while to sketch the graph each time.

Example: Graph 1 full period of: .

1. Parent-Sketch the parent graph of the cosine function.

x / y
0 / 1
90 / 0
180 / -1
270 / 0
360 / 1

2. Amplitude- Multiply ‘y’ times ‘a’. Record in the chart.

3. Period- Divide each ‘x’ by ‘b’. Record in the chart.

/ y*a
0 / -2
45 / 0
90 / 2
135 / 0
180 / -2

4. Phase Shift – Add ‘-c/b’ to ‘x’ from step 3.

5. Vertical Shift – Add ‘d’ to ‘y’ values. This is the final graph that will be scaled and drawn on graph paper.

/ y+d
-30 / 0
15 / 2
60 / 4
105 / 2
150 / 0