CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 5. Trigonometric Functions

TABLE5.8:(continued)

50 42

65 2

William chooses to see a negative cosine in the graph. He identifies the amplitude to be 40 feet. The vertical shift
of the sinusoidal axis is 42 feet. The horizontal shift is 5 minutes to the right.
The period is 60 (not 65) minutes which impliesb=6 when graphed in degrees.
60 =^360 b
Thus one equation would be:
f(x) =− 40 ·cos( 6 (x− 5 ))+ 42
Concept Problem Revisited
The functionf(x) = 2 ·sinxcan be rewritten an infinite number of ways.

2 ·sinx=− 2 ·cos

(

x+π 2

)

= 2 ·cos

(

x−π 2

)

=− 2 ·sin(x−π) = 2 ·sin(x− 8 π)

It all depends on where you choose start and whether you see a positive or negative sine or cosine graph.

Vocabulary

Phase shiftis a typical horizontal shift left or right that is used primarily with periodic functions.

Guided Practice

1. Tide tables report the times and depths of low and high tides. Here is part of tide report from Salem, Massachusetts
   dated September 19, 2006.

TABLE5.9:

10:15 AM 9 ft. High Tide

4:15 PM 1 ft. Low Tide

10:15 PM 9 ft. High Tide 261