All Four at Once
Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 33 of 51.
When the wave is shifted as well, write it as y = a sin(b(x − h)) + k with a and b positive, and read all four. Heights give k and a; the period gives b; and h is where the wave crosses its midline going up. Pick the first such crossing at or to the right of 0 so the answer is unique.
This wave runs from −1 to 3: k = 1 and a = 2. Its tops are 180° apart, so b = 360° ÷ 180° = 2. It crosses its midline going up at 45°, so h = 45°:
y = 2sin(2(x - 45°)) + 1
Keep b outside the bracket: 2(x − 45°) shows the shift; 2x − 90° hides it.
Challenge
Write the equation of the wave in the graph tile in the form y = a×sin(b(x - h)) + k, with a and b positive, b outside the bracket, and h the first crossing going up at or right of 0. 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