Tangent Equations
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 21 of 56.
Solve tan(x) − √3 = 0: tan(x) = √3, and tan 60° is √3, so 60° is one answer. Tangent is positive in quadrants I and III, so the other is 180° + 60°, which is 240°.
The two are exactly 180° apart because tangent is y/x: half a turn on, both coordinates flip sign and the ratio stays the same. Find one answer, add 180°.
Challenge
Solve tan(x) + 1 = 0 for every x in [0°, 360°), then press Check.
Try it yourself
tan(x) + 1 = 0
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 Domain