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