Chapter 17: Trigonometric and Transforming graphs

Graphs

• You need to recognise and be able to sketch the graphs of the trigonometric functions sin,cos and tan
• y=sinx and y=cosx
  • y = sinx and y=cosx have the same shape
  • y = sinx is y=cosx translated by 90 to the right
  • y = cosx is symmetrical about the y-axis
  • y = sinx is symmetrical about the line x = 90
• y=tanx
  • y=tanx repeats every 180
  • There are asymptotes at -90,90,270…
  • The graph gets closer to these asymptotes but never reaches them

Sketching a trig graph

• Label the x-axis in multiples of 90
• For sin and cos label the y-axis from -1 to 1
• For tan label the y-axis from -3 to 3
• Mark some values that you know on your graph

Transforming graphs

• You can change the equation of a graph to translate or reflect it
• The easiest way to describe these transformations is using function notation
• The tables show transformation of the graph y=f(x)
  • y=f(x) + a
  • translation (o/a)
  • f(x) + a ------ move up x units
  • f(x) - a ------ move down x units
  • y=f(x+a)
  • translation (-a/o)
  • f(x+a) -------- move left x units
  • f(x-a) ---------move right x units
  • y=-f(x)
  • reflections in the x-axis
  • ‘___’ outside the bracket
  • y=f(-x)
  • reflection in the y-axis
  • ‘____’ inside the bracket

Sin and cos

• The graph of y=sinx is a translation of y=cosx by 90 to the right
• This means that y=sinx is the same as y=cos(x-90)