Negative Angles
Part of the Trig Identities section of Coddy's Trigonometry journey. Lesson 15 of 52.
A negative angle turns clockwise. The point at -30° is the point at 30° reflected in the x-axis: the same distance across, the same distance down as the other is up.
Reflecting in the x-axis keeps x and flips the sign of y.
So cos(-30°) = √(3)/2, the same as cos 30°, while sin(-30°) = -1/2, the opposite of sin 30°. The reflection works for every angle, which gives three identities (the last wherever tan x is defined):
cos(-x) = cos(x)
sin(-x) = -sin(x)
tan(-x) = -tan(x)
A function that ignores the sign of its angle, like cosine, is called even; one that passes the sign through, like sine and tangent, is odd.
Challenge
Set the coordinates of the point at -60°. Then 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 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