Graphing Trigonometric Functions



Graphing Trigonometric Functions

The graph of sinx and cosx and transformations of these graphs are collectively called sine waves or sinusoids.

Amplitude of a graph is ½ the difference between the maximum and minimum.

Period is how long it takes the graph to repeat. (1 time around a circle = 2()

A horizontal translation of a sine or cosine graph is called a phase shift.

In the general form y = asin(bx – h) +k

y = acos(bx – h) +k

k is the vertical shift, h is the horizontal (phase) shift, the amplitude is the | a |, and the period is [pic].

Examples:

1. Find the period of each function in

radians, and the amplitude.

A) y = 2sinx

B) y = -3cos(8x)

C) y = -5sin[pic]

D) y = [pic]cos[pic]

Examples:

Graph the following function from -[pic] to [pic]. (begin by listing period and amplitude)

2. y = sinx

3. y = cosx

4. y = tanx

5. y = 2sinx

6. y = 3cosx

7. y = -½cosx

8. y = cos[pic]

9. y = sin 2x

10. y = cos4x

11. y = sinx + 2

12. y = cosx – 1

13. y = 2cosx + 1

-----------------------

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

-2 π -[pic] π -[pic] [pic] π [pic] 2π

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