Families in Radians
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 33 of 56.
In radians a full turn is 2π. cos(x) = 1/2 has π/3 and 5π/3 in one turn, so every solution is
x = π/3 + 2π·k
x = 5π/3 + 2π·k
The second family is the same as −π/3 + 2πk: 5π/3 is −π/3 plus one turn. Books often write the pair as ±π/3 + 2πk. Any base works, as long as the period is 2π for sine and cosine and π for tangent.
Challenge
Find every solution of 2sin(x) + √2 = 0 in radians, with k any integer, and press Check.
Try it yourself
2sin(x) + sqrt(2) = 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: Compositions7General Solutions
Every SolutionTangent's Single FamilyFamilies in RadiansFamilies, RoundedRecap: Every Solution2Inverses 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