Half Angles
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 38 of 56.
A half angle runs the other way. In 2sin(x/2) = 1, while x runs over [0°, 360°), x/2 runs over [0°, 180°): only half a turn. sin(x/2) = 1/2 at x/2 = 30° or 150°, both in that half turn, so x = 60° or 300°.
A half turn can also hold fewer answers than a full one. cos(x/2) = −1/2 needs x/2 = 120° or 240°, and only 120° is below 180°: one answer, x = 240°.
Challenge
Solve 2cos(x/2) = √2 for every x in [0°, 360°), then press Check.
Try it yourself
2cos(x/2) = sqrt(2)
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