Reciprocals in Radians
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 50 of 57.
Radians change nothing. Take csc(7π/4): 2π − π/4, quadrant IV, reference π/4. Sine is negative there, so csc(7π/4) = -csc(π/4), and sin(π/4) = √2/2 flips to 2/√2 = √2. The value is −√2.
Cotangent flips tangent: cot(π/6) is 1/(√3/3), which is √3, and cot(π/4) is 1. Where tangent is undefined, at π/2, cotangent is 0, because cos/sin is 0/1 there.
Challenge
Work out cot(2π/3) exactly, then press Check.
Try it yourself
cot(2pi/3)
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: Radians7Reference Angles and Signs
Reference AnglesReference in III and IVSigns by QuadrantSign and SizeSigns at Any AngleRecap: Reference Angles10Six Functions, Any Circle
Any Circle, Any RadiusFrom a Point to the AngleSecant, Cosecant, CotangentReciprocals in RadiansRecap: Six Functions5Arc Length and Sector Area
Arc LengthArcs From DegreesFinding the AngleSector AreaRecap: A Slice of Pizza