Secant, Cosecant, Cotangent
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 49 of 57.
Each of the three has a reciprocal with a name: sec(θ) = 1/cos(θ), csc(θ) = 1/sin(θ) and cot(θ) = cos(θ)/sin(θ). On the unit circle that is 1/x, 1/y and x/y. The names pair crosswise: secant goes with cosine, cosecant with sine. Each pair has exactly one "co".
To find one at any angle, find its partner, then flip. sin(150°) = 1/2, so csc(150°) = 2. Flipping never changes a sign, so each reciprocal has its partner's sign in every quadrant.
Flipping 0 is impossible: secant is undefined where cosine is 0 (90°, 270°), cosecant and cotangent where sine is 0 (0°, 180°).
Challenge
Work out sec(240°) exactly: use the reference angle, then the value. Then press Check.
Try it yourself
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