Two Turns, Four Answers
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 23 of 56.
A domain is not always one turn. On [0°, 720°), tan(x) = √3 has 60° and 240° in the first turn; add 360° to each for the second, 420° and 600°. Four answers in two turns.
On [−180°, 180°) the turn starts at −180°: the same points, but named so they fall inside, so 240° is written −120°. Find the answers in one turn, then add or subtract 360° until every one lies in the domain asked.
Challenge
Tap every angle θ in [0°, 720°) with cos(θ) = √3/2. Use the Turn switch for the second turn, 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 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 Domain