7 ­ Transformations of Trig Graphs.notebook
September 03, 2014
Graphing Trigonometric Functions
EQ: How do I graph a periodic function?
MCC9­12.F.IF.7e Graph trigonometric functions showing period, midline, and amplitude.
Sep 2­5:32 PM
Vocab
Sinusoidal Axis - the axis that is the midpoint
of a sine or cosine curve.
Sep 2­5:33 PM
1
7 ­ Transformations of Trig Graphs.notebook
September 03, 2014
General Form of Periodic Functions
y = A sin (bx ­ c) + d
or
y = A sin (b(x ­ c/b)) + d
Amplitude = Period =
Phase Shift =
Vertical Shift =
Sep 2­5:35 PM
Example 1: y = 4 cos (3x)
Amplitude:
Period:
Phase Shift:
Vertical Shift:
Sep 2­5:48 PM
2
7 ­ Transformations of Trig Graphs.notebook
Example 2: September 03, 2014
y = 3 sin (x) ­ 2
Amplitude:
Period:
Phase Shift:
Vertical Shift:
Sep 2­5:48 PM
Example 3: y = 1/2 cos (2x ­ π/3) ­ 1
Amplitude:
Period:
Phase Shift:
Vertical Shift:
Sep 2­5:48 PM
3
7 ­ Transformations of Trig Graphs.notebook
Example 4: September 03, 2014
y = ­5 sin (1/3x ­ π/6)
Amplitude:
Period:
Phase Shift:
Vertical Shift:
Sep 2­5:48 PM
Determine the amplitude and period of the following functions. Then, describe any phase or vertical shifts.
1. 4 sin (x)
2. 3 cos (x) ­ 2
3. 4 sin (3x)
4. ­3 cos (x ­ π/4)
5. 1/2 sin (2x) + 5
6. 5/2 cos (2x ­ π/3)
7. tan (2x)
8. tan (3x + π/4)
9. 2 sin (4x + π) ­ 1
10. 8 cos (1/2x ­ π/3)
Sep 2­5:37 PM
4
7 ­ Transformations of Trig Graphs.notebook
September 03, 2014
Graph the following function:
y = sin (3x)
Amplitude:
Sinusoidal Axis:
Period:
Phase Shift:
Sep 2­5:45 PM
Graph the following function:
y = 2 cos (x) ­ 1
Amplitude:
Sinusoidal Axis:
Period:
Phase Shift:
Sep 2­5:45 PM
5
7 ­ Transformations of Trig Graphs.notebook
September 03, 2014
Graph the following function:
y = ­cos (3x­π/2) + 1
Amplitude:
Sinusoidal Axis:
Period:
Phase Shift:
Sep 2­5:45 PM
Graph the following function:
y = tan (2x­π/2) + 1
Amplitude:
Sinusoidal Axis:
Period:
Phase Shift:
Sep 2­5:45 PM
6