Graphing Trigonometric Functions with Translations and Asymptotes

Key Questions

  • What is meant by the amplitude of a trigonometric function?

    The amplitude is the distance from the midline to the maximum or to the minimum (they are the same). For example, #y = sin(x)# has an amplitude of 1 because the midline is #y=0# and the max is 1.

    This can be found by finding the range of the function and dividing by two. (See if you can figure out why.)

    Anthony X · 1 · Feb 11 2016
  • Which Trig functions have asymptotes?

    #tanx#, #cotx#, #secx#, and #cscx# have vertical asymptotes.

    I hope that this was helpful.

    Wataru · 5 · Oct 30 2014
  • How do I horizontally translate a trigonometric graph?

    By changing the "c" in your basic trigonometric equation.

    The standard trig equation for sine is #y=a*sin[b(x-cpi)]+d#. In this, the variable #a# represents the amplitude. The variable #b# represents the period (#(2pi)/b# = period). Now, the variable #c# represents what is known as the phase shift - more commonly known as a horizontal translation. You shift the graph #cpi# units from the original parent function, which in this case is #y=sinx#. If #c# is positive, shift the graph to the right #cpi# unites. If #c# is negative, shift the graph to the left #cpi# units.

    If you're wondering, #d# represents the vertical translation.

    I hope this helps, and I'f strongly suggest going to google and typing in functions like #y=sin(x-2pi)# and comparing them to the parent function, #y=sinx#.

    lagann46 · 3 · Nov 17 2014

Questions

Graphs of Trigonometric Functions