Graphing Trigonometric Functions

Graphing Trigonometric Functions by hand (sine and cosine):
  1. Identify the amplitude of the trigonometric function.
  2. Identify the frequency of the trigonometric function.
  3. Identify the period of the trigonometric function.
    • Note: If you are not sure what amplitde, frequency, and/or period is, please view the Web pages on them.
  4. Set up your graph paper.
    • Every 6 lines on your graph paper, place a tick mark for your x-values.
    • Every 4 lines on your graph paper, place a tick mark for your y-values.
    • To check for tick marks that will have a coordinate point, you must take 6/frequency and it will tell you if you need more tick marks, if you do then it will tell you the spacing and it will also tell you which tick marks will get a coordinate point.
      • Example: If 6/frequency equals 3, then every third line along the x-axis will have a tick mark and a coordinate point.
      • Example: If 6/frequency equals 12, then not every tick mark will have a coordinate point along the x-axis, every other tick mark will have a coordinate point (ie. 0, π, 2π)
  5. Start graphing the trigonometric function along the y-axis.
    • For the sine function, you will start graphing at the origin (0,0).
    • For the cosine function, you will start graphing at the a value of the trigonometric function.
Graphing Trigonometric Functions on the Graphing Calculator (TI-83 or TI-84):
  1. Set your mode to degree
    • Select mode and make sure degree is highlited. If not, arrow down to degree and press Enter.
    • You want to graph in degree mode, even though we graph by hand usually in radians because radian mode will give you decimals instead of fractions, but we can then take the degree measure and convert it to radians by multiplying by π/180°.
  2. Go the the y= screen and type on your equation into y1.
  3. Set up the viewing window.
    • Zoom, 7 (ztrig)
    • This window will graph from x = -360° to x =  360°
    • Once you press Zoom, 7, the graphing calculator will automatically graph the function.