1. Trigonometric Functions
Graphing the Trigonometric Function

2. Graphing Trigonometric Functions
Amplitude: the maximum or minimum vertical distance between the graph and the x-axis. Amplitude is always positive 2

3. If |a| > 1, the amplitude stretches the graph vertically.
The amplitude of y = a sin x (or y = a cos x) is half the distance between the maximum and minimum values of the function.
amplitude = |a|
If |a| > 1, the amplitude stretches the graph vertically.
If 0 < |a| < 1, the amplitude shrinks the graph vertically.
If a < 0, the graph is reflected in the x-axis. y x
y = 2sin x
y = sin x
y = sin x
y = – 4 sin x
reflection of y = 4 sin x
y = 4 sin x
Amplitude

4. Trigonometric Functions
Period: the number of degrees or radians we must graph before it begins again. 4

5. If b > 1, the graph of the function is shrunk horizontally.
The period of a function is the x interval needed for the function to complete one cycle.
For b  0, the period of y = a sin bx is
For b  0, the period of y = a cos bx is also
If 0 < b < 1, the graph of the function is stretched horizontally. y x
period:
period: 2
If b > 1, the graph of the function is shrunk horizontally. y x
period: 4
period: 2
Period of a Function

6. Sine Function Quick Facts
y = sinx

7. Cosine Function Quick Facts
y = cosx

8. Find the properties given the trigonometric function:
y = 2sinx 3. y = cos(4x)
Amplitude: Amplitude:
Period: Period:
y = 3sin(2x) 4. y = 6cos(½x)

9. Identify the properties of the graph
Amp=
Period=
Equation=

10. Identify the properties of the graph
Amp=
Period=
Equation=

11. Identify the properties of the graph
Amp=
Period=
Equation=

12. Identify the properties of the graph
Amp= Period= Equation=