Tangent in Radians
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 44 of 57.
In radians tangent repeats every π. At π/4 it is 1, at π/3 it is √3, at π/6 it is √3/3, and it is undefined at π/2 and 3π/2.
Take tan(7π/4): 2π − π/4, quadrant IV, reference π/4. Tangent is negative in IV, so tan(7π/4) = -tan(π/4), which is −1.
Same two questions, same chip: reference angle first, then the value.
Challenge
Work out tan(5π/6) exactly, then press Check.
Try it yourself
tan(5pi/6)
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Angles and the Unit Circle
1A Point on a Circle
Height on the CircleAcross: the CosineSame Height, Two AnglesRecap: Height and Across4Radians
What a Radian IsDegrees to RadiansRadians to DegreesRadians Without πTurns in RadiansRecap: Radians5Arc Length and Sector Area
Arc LengthArcs From DegreesFinding the AngleSector AreaRecap: A Slice of Pizza3Coterminal Angles
Coterminal AnglesBack Into One TurnValues Repeat Every TurnEvery Turn at OnceRecap: Coterminal Angles6The Unit Circle
Why (cos θ, sin θ)The 30° and 60° PointsThe 45° PointPoints Off the TableRecap: Quadrant I Points9Tangent on the Circle
Tangent Is y over xWhere Tangent Is UndefinedTangent in RadiansEvery Angle for a TangentRecap: Tangent