Trigonometric Graphs

Notes:

If you look at the Unit Circle, you’ll see that it starts at point (0,0), and then it ends after a period of 2π.

So a usual graph would begin at (0,0) and end at 2π. However, not all graphs do this.

A trigonometric graph would usually look like this:

f(x) = (a)sin(bx - c)

So… that’s nice to know and all, but what things do we look for in a trigonometric graph?

  • Domain

  • Range

  • Period

  • Odd or Even function

And… if the question demands it…

  • Amplitude

  • Phase Shift

Terms

  • Amplitude: ‘a’ (going up & down)

  • Period: (2π / b)

    • Proof: bx - c = 2π => x = (2π + c / b)

  • Phase shift: (c / b)

    • Proof: bx - c = 0 => x = (c / b)