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Understanding Period and Amplitude in Trigonometric Graphs, Schemes and Mind Maps of Physics

University of Northern Iowa (UNI)Physics

The concepts of period and amplitude in trigonometric graphs, using examples of sin and cos functions. It covers the rules for transforming trig graphs and provides exercises for practice.

Typology: Schemes and Mind Maps

2021/2022

Uploaded on 09/27/2022

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Amplitude and Period for
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Download Understanding Period and Amplitude in Trigonometric Graphs and more Schemes and Mind Maps Physics in PDF only on Docsity!

Amplitude and Period for

Graphs

Period and Amplitude A graph which consists of the same basic pattern repeated over and over is called periodic. The period is the horizontal coverage of the basic pattern. The amplitude of a graph is half of its vertical coverage. y = sin x 360

Period Amplitude

Heinemann, p.53, EX 4A (ORALLY)

Graphing trig functions Recall the rules for transforming graphs. The same rules apply for trig graphs:

Example 1 Sketch and annotate the graph of 0

y = 2sin x + 3

Solution: Graphing trig functions

  1. Amplitude = 2 so vertical extent = 4
  2. b = 1 so period = 360 0
  3. Normally sin x graph starts at 0, so this graph starts at +3. 0  x  360

0

y = 2sin x + 3

0 180 0

0

0

  1. Amplitude = 2 so vertical extent = 4
  2. b = 1 so period = 360 0
  3. Normally sin x graph starts at 0, so this graph starts at +3.

Example 2 Write a trig function represented by this graph: (^30) 180 360 540 720

  1. Cos graph
  2. a = ½ of vertical extent = 3
  3. b = no of complete waves in 360 0 = 1
  4. Axis of symmetry is now 1 so graph moved up by 1
    1. Graph has moved right by 30 0 **Equation is y = 3 cos (x – 30) 0
  • 1**

Heinemann, p.54, EX 4B Q1 & Q