Pick the Right cos 2x
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 48 of 56.
cos 2x has three forms: cos(x)² − sin(x)², 2cos(x)² − 1 and 1 − 2sin(x)². Pick the one in the same function as the rest of the equation, so one function is left.
In cos(2x) = cos(x) the rest is in cosine, so use 2cos²x − 1: 2cos(x)² − cos(x) − 1 = 0. That is a quadratic in cos x, (2cos(x) + 1)(cos(x) − 1) = 0, so cos x = −1/2, giving 120° and 240°, or cos x = 1, giving 0°.
Challenge
Solve cos(2x) = sin(x) for every x in [0°, 360°), then press Check.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Trig Equations and Inverses
1Your First Trig Equations
One Equation, Two AnglesReading Signs on the CircleThe Reference AngleRecap: First Equations4Compositions
Draw the TriangleThe Outer FunctionA Negative InsideWhen Undoing Does Not UndoRecap: Compositions7General Solutions
Every SolutionTangent's Single FamilyFamilies in RadiansFamilies, RoundedRecap: Every Solution10Identities First
Write sin 2x OutPick the Right cos 2xSwap cos²x for sin²xsec, csc and cotRecap: Identities First2Inverses and Their Ranges
Why arcsin Gives One AngleNegative Inputs to arcsinThe Range of arccosThe Range of arctanRecap: Inverse Ranges5Equations on a Domain
A Negative CosineTangent EquationsEquations in RadiansTwo Turns, Four AnswersRecap: On a Domain