Sinusoidal Functions & Graphs (DP IB Applications & Interpretation (AI)): Revision Note

Sinusoidal Functions & Graphs

What are the key features of sinusoidal graphs?

• A sinusoidal graph is of the form

  • 

  • 

• The y-intercept is at the point where x = 0

  • (0, -asin(bc) + d) for 

  • (0, acos(bc) + d) for 

• The period of the graph is the length of the interval of a full cycle

  • This is  (in degrees) or 

• The maximum value is y = a + d

• The minimum value is y = -a + d

• The principal axis is the horizontal line halfway between the maximum and minimum values

  • This is y = d

• The amplitude is the vertical distance from the principal axis to the maximum value

  • This is a

• The phase shift is the horizontal distance from its usual position

  • This is c