Cambridge O Level Additional Mathematics · Syllabus 4037 · Trigonometry
Reciprocal Trigonometric Functions
What is Reciprocal Trigonometric Functions?
Secant, cosecant and cotangent are the three reciprocal trigonometric functions, defined as sec theta = 1/cos theta, cosec theta = 1/sin theta and cot theta = 1/tan theta = cos theta/sin theta. Each is undefined wherever its denominator is zero, and each carries the same sign as the function it is the reciprocal of. They are reciprocals, not inverse functions: sec theta returns a ratio, whereas the inverse function cos to the power minus one returns an angle.
This definition is part of the Trigonometry chapter in Cambridge O Level Additional Mathematics.
Questions students ask about Reciprocal Trigonometric Functions
What are the reciprocal trigonometric functions?
Secant, cosecant and cotangent are defined as \(\sec\theta=\dfrac1{\cos\theta}\), \(\operatorname{cosec}\theta=\dfrac1{\sin\theta}\) and \(\cot\theta=\dfrac{\cos\theta}{\sin\theta}\). Each is undefined wherever its denominator is zero, and each carries the same sign as the function it is the reciprocal of. They are reciprocals, not inverse functions: \(\sec\theta\) takes an angle and returns a ratio, whereas \(\cos^{-1}\theta\) takes a ratio and returns an angle, so the two are never interchangeable.