Equations in Radians
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 22 of 56.
On [0, 2π) nothing changes but the units: π takes the place of 180°. Solve 2sin(x) − √2 = 0: sin(x) = √2/2, the reference angle is π/4, and the quadrant II partner is π − π/4. Write π as 4π/4: four quarters minus one is three quarters, so x = π/4 or 3π/4.
The partners in radians: quadrant II is π − r, quadrant III is π + r, quadrant IV is 2π − r.
Challenge
Solve 2sin(x) + √3 = 0 for every x in [0, 2π). Give the answers as fractions of π 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 Domain