Every Solution of sin 3x
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 39 of 56.
For every solution of sin(2x) = 1/2, write the families for 2x first: 2x = 30° + 360°·k or 2x = 150° + 360°·k. Then divide everything by 2, the period too:
x = 15° + 180°·k
x = 75° + 180°·k
The most common slip is halving the 30° and keeping 360°k. That family misses 195° and every other answer. A multiple angle shrinks the period: sin 2x repeats every 180°, sin 3x every 120°.
Challenge
Find every solution of 2sin(3x) = 1, with k any integer, and 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: Compositions2Inverses 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 Domain8Multiple Angles
Two Turns for 2xSolving sin 2xHalf AnglesEvery Solution of sin 3xRecap: Multiple Angles