Even and Odd Graphs
Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 17 of 52.
The identities show in the graphs. Cosine is even, so its graph is the same on both sides of the y-axis: fold the page along the axis and the halves match. That is what cos(-x) = cos(x) says: the height at -x is the height at x.
y = cos x: a mirror image across the y-axis.
Sine is odd. Its height at -x is minus its height at x, so the left half is the right half turned upside down: a half turn about the origin carries the graph onto itself. Drawing y = cos(-x) therefore gives the cosine wave again, unchanged.
Challenge
Draw the graph of y = sin(-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 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