The Equation of a Wave
Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 30 of 51.
Four readings turn a drawn wave into an equation, always in this order. Heights first: the midline k is halfway between the highest and lowest values, and the amplitude is half the gap. Then lengths: measure the period from one top to the next and turn it into b = 2π ÷ period. Last, look at x = 0 to choose sine or cosine and the sign of a: a wave with no shift is at a top, a bottom or its midline there.
This wave runs from −2 to 4, so k = 1 and the amplitude is 3. The tops are π apart, so b = 2π ÷ π = 2. At x = 0 it is on its midline going up, which is a sine with a positive a:
y = 3sin(2x) + 1
Challenge
Write the equation of the wave in the graph tile in the form y = a×cos(b×x) + k, with b a whole number. Press Check.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Graphs of Trig Functions
1From Circle to Wave
Ride a Ferris WheelHeight on the Unit CircleUnrolling the Sine GraphThe Sine Graph in RadiansCircle to Wave Recap7Reading a Graph
The Equation of a WaveSine or Cosine?From Peaks to a WaveAll Four at OnceReading Recap