Sine or Cosine?
Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 31 of 51.
Every sine or cosine wave can be written both ways. The wave with a top at 0 is y = 2cos(x), and it is also y = 2sin(x + pi/2): the same curve. Which one to write depends on what the question asks for, and on what is simplest.
Look at x = 0. If the wave is at a top or a bottom there, a cosine needs no shift: a top means a positive a, a bottom a negative a. If it is on its midline there, a sine needs no shift: going up means a positive a, going down a negative a.
If the question asks for the other function, you need a shift to make it fit.
Challenge
Write the equation of the wave in the graph tile as a sine, in the form y = a×sin(b×x) 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