Periods & Amplitudes (Cambridge (CIE) IGCSE International Maths)

Periods & Amplitudes

What are oscillating graphs?

• The sine and cosine graphs are oscillating graphs

  • Both graphs oscillate between a maximum and a minimum point

  • A cycle is completed when the graph returns an initial starting point

  • The cycle is repeated indefinitely in both the positive and negative x directions

What are the features of oscillating graphs?

• An oscillating graph has the following key features:

  • The amplitude is half the vertical distance from the maximum point to the minimum point

    • This is the distance from the horizontal line of symmetry (often the x-axis) to the minimum or maximum point

  • E.g. For the graph the amplitude is 1

• The period is the distance along the x-axis to complete a full oscillation

  • Maximum point to maximum point

  • Minimum point to minimum point

  • x-intercept to next but one x-intercept

  • E.g. For the graph the period is 360º

How do I draw an oscillating graph from its equation?

• An oscillating function has equation

  • 

  • 

• The represents the amplitude of the function

  • The bigger the value of the bigger the range of values of the function

  • E.g. For the graph

    • The amplitude is 5 units

    • The distance from the x-axis (horizontal line of symmetry) to the maximum/minimum point would be 5 units

  • E.g. For the graph

    • The amplitude is of a unit

    • The vertical distance from the line to the maximum/minimum point would be of a unit

• The determines the period of the function

  • The bigger the value of the quicker the function repeats a cycle

  • The period is 

    • A larger value of produces a shorter period

  • E.g. For the graph

    • The period is

    • The graph has been 'squashed' by a factor of 2 horizontally

    • Two complete cycles will occur in an interval of

  • E.g. For the graph

    • The period is

    • The graph has been 'stretched'

    • Half a cycle will occur in an interval of