The Graph of 2 sin x cos x
Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 36 of 52.
The double-angle formulas turn some products and squares of waves into a single wave. cos(x)² - sin(x)² is cos(2x): a cosine squeezed to twice the speed, one full wave every π.
y = cos²x - sin²x is y = cos 2x.
Doubling the angle halves the period: 2π becomes π. The height does not change, because the 2 sits inside the angle, not in front of the function.
Challenge
Draw the graph of y = 2sin(x)cos(x). 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 Angles7Double-Angle Formulas
sin 2x = 2 sin x cos xThree Forms of cos 2xExact Values, DoubledSquare, Then DoubleThe Graph of 2 sin x cos xRecap: Double 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