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:
- y = a⋅sin(bx + c) + d
- y = a⋅cos(bx + c) + d
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: