Graphs of Trig Functions Unit #4, Lesson 6

30° 60° 120° 150° 210° 240° 300° 330° 90°180°270° 360° 1

30° 60° 120° 150° 210° 240° 300° 330° 90°180°270° 360° 1

30° 60° 120° 150° 210° 240° 300° 330° 90°180°270° 360° 1

30° 60° 120° 150° 210° 240° 300° 330° 90°180°270° 360° 1

30° 60° 120° 150° 210° 240° 300° 330° 90°180°270° 360° 1

30° 60° 120° 150° 210° 240° 300° 330° 90°180°270° 360° 1

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Cosine

Other Trig Function Graphs

TRANSFORMATIONS OF SINE AND COSINE GRAPHS Moving on…

Amplitude Half the distance between the maximum and minimum values of the graph of the function. The amplitude of the graphs of y=asinx and y=acosx is |a|. What if “a” is a negative number?

For Example: This is the graph of sin(x)

For Example: And this is the graph of 3sin(x)

Period One complete repetition of the pattern is called a cycle. The period of a function is the horizontal length of one complete cycle. The formula for calculating the period of the graphs of y=sin(bx) and y=cos(bx) is.

For Example: This is the graph of sin(x)

For Example: And this is the graph of sin(2x)

Phase Shift The horizontal shift of a graph. The phase shift of the graphs of y=sin(bx-c) and y=cos(bx-c) is c/b. Watch your signs!

For Example: f(t) = sin(t – π/3)

Vertical Shift The vertical shift of the graphs of y=sinx+d and y=cosx+d is d.

For Example: This is the graph of sin(x)

For Example: And this is the graph of sinx + 3

For the graph of the function, find the following: Amplitude: Period: Phase Shift: Vertical Shift:

For the graph of the function, find the following: Amplitude: |3| = 3 Period: Phase Shift: Vertical Shift:

For the graph of the function, find the following: Amplitude: |3| = 3 Period: Phase Shift: Vertical Shift:

For the graph of the function, find the following: Amplitude: |3| = 3 Period: Phase Shift: Vertical Shift:

For the graph of the function, find the following: Amplitude: |3| = 3 Period: Phase Shift: Vertical Shift: 1