sin²x Is a Wave
Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 39 of 52.
cos(x)² = 1/2 + cos(2x)/2. Read it as a graph: a cosine wave of height 1/2, twice the usual speed, lifted so that its midline is 1/2. It runs between 0 and 1, never below 0, which is right for a square.
y = cos²x: midline 1/2, height 1/2, one wave every π.
The square of a wave is a wave. Its midline is the average of the square, 1/2, and its period is half the original, because squaring makes the negative half of each wave look like the positive half.
Challenge
Draw the graph of y = sin(x)². Then press Check.
Try it yourself
Draw the graph
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Trig Identities
1Identities on the Circle
sin²x + cos²x = 1Squares Erase the SignsIdentity or Equation?Recap: the Circle Identity4Even, Odd and Cofunctions
Negative AnglesEven and Odd in a ProofEven and Odd GraphsCofunctionsRecap: Signs of Angles2Reciprocal and Quotient
The Quotient IdentitySecant, Cosecant, CotangentDividing by a FractionWhere They BreakRecap: Reciprocals5Proving Identities
Work on One SideRewrite in sin and cosFactor FirstMake One FractionProofs That Go WrongRecap: Prove It8Half Angles, Power Reduction
Power Reductionsin²x Is a WaveHalf-Angle Valuestan of a Half AngleRecap: Half Angles