sec, csc and cot
Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 50 of 56.
csc(x) = 2 is a sine equation in disguise: csc x = 1/sin x, so sin x = 1/2, and the answers are 30° and 150°. Secant turns into cosine and cotangent into tangent the same way: flip the value. For cotangent the value must not be 0: cot x = 0 at 90° and 270°, where tan x has no value.
The flip also rules values out. sin x and cos x stay in [−1, 1], so sec x and csc x are never strictly between −1 and 1: sec x = 1/2 has no solution, since cos x would be 2.
Challenge
Solve sec(x) + 2 = 0 for every x in [0°, 360°), then 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: Compositions7General Solutions
Every SolutionTangent's Single FamilyFamilies in RadiansFamilies, RoundedRecap: Every Solution10Identities First
Write sin 2x OutPick the Right cos 2xSwap cos²x for sin²xsec, csc and cotRecap: Identities First2Inverses 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