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

Graphs of trigonometric functions

What are the properties of the graphs of y = sin x and y = cos x?

• The graphs of sin x and cos x are very similar

  • They are transformations of each other

• They intersect the y-axis at different places

  • sin x passes through the origin

  • cos x passes through (0, 1)

• Both graphs have the same domain and range

  • Domain: 

  • Range: 

• The graphs are both periodic

  • They repeat every 360° (2π radians)

• The amplitude of the graphs of sin x and cos x is 1

What are the properties of the graph of y = tan x?

• The graph of tan x intersects the y-axis at the origin

• The graph is undefined at the points ± 90°, ± 270° etc

  • There are asymptotes at these points on the graph

  • In radians this is at the points ± , ± etc

• The domain and range of the graph is

  • Domain:  

  • Range: 

• The graph of tan x is periodic

  • It repeats every 180° (π radians)

How do I sketch trigonometric graphs?

• STEP 1
  Check whether you are working in degrees or radians

  • Check the domain given for this

• STEP 2
  Label the x-axis in multiples of 90° (or )

  • Make sure you cover the whole domain on the x-axis

• STEP 3
  Label the y-axis

  • Use – 1 ≤ y ≤ 1 for sin or cos

  • Use the whole y-axis for tan

• STEP 4
  Identify what happens at each multiple of 90° (or )

  • sin0=0, cos0=1, tan0=0

  • sin90=1, cos90=0, tan90 is undefined

  • etc

• STEP 5
  Draw the graph using the general shape