This document provides instructions for graphing trigonometric transformations in 3 steps: 1) Determine the a, b, c, and d values from the function's factored form. 2) Draw the median position and amplitude. 3) Determine the period and mark points to graph the wave-like function. Examples graph y=3sin(2x)-1, f(x)=sin(1/2x+1), and f(x)=2cos(3x)-2.

1. Exercise #13
Graphing Trigonometric Transformations
f ( x) sin x f ( x) cos x
Before graphing trigonometric functions, they must be in factored form!
y a sin(b( x c)) d
Example
Graph y 3sin 2 x 1 . To graph trigonometric functions, follow the steps below:
2
Step 1
Determine the values for a, b, c and d.
a =
d=
b=
c=
Step 2
Draw the median position using a broken line (dotted).
y
x
Step 3
Draw the maximum and minimum values, using the amplitude.

2. Step 4
Determine the period and divide it into four equal parts.
Step 5
Start drawing the graph at c and follow by marking off 5 points.
y
x
Example
1
Graph f ( x) sin x 1
2 2
y
x

3. Example
Graph f ( x) 2cos 3x 2
y
x