Writing Sinusoidal Equations without a Graph

Oftentimes you’ll be presented with the properties of the wave and will be expected to create an equation from them. For example, you may be given the amplitude, period, phase-shift or told that it reflects about the x axis or has a height of n. Whatever the case is, you always start one of the general formulas:

  1. asin(bcd
  2. acos(bcd

Some general tips to follow:

  • If given the amplitude or height, begin by filling in the factor a first.
  • If given the period and phase-shift, you need to find the value b using the period before you can find the value for c.
  • If the period and phase-shift is given without units (such as degrees °), the equation is in radians.
  • Always have a summary of the formulas ready or memorized: