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This topic covers differentiating and working with the reciprocal trigonometric functions sec x, cosec x and cot x, including their derivatives and the identities connecting them to tan. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Rewrite sec, cosec and cot in terms of cos, sin and tan, or learn their derivatives directly. The negatives on cosec and cot are what catch people out, so note them before you start.
Before you start
It assumes you can handle trigonometric identities and differentiation. The same ideas return in harder calculus with trigonometry. It belongs to the Pure 3 specification.
What you learn
Each has its own standard derivative. This lesson establishes all three, extends them to multiples and composites with the chain rule, combines them with the product and quotient rules, and applies them to gradients and tangents. The reciprocal-trig derivatives slot into the product and quotient rules just like any other function. The course works through the three standard derivatives, multiples of the angle, the chain rule with a function inside, combining with product and quotient rules and gradients, tangents and identities. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Reciprocal Trig is part of the Differentiation strand of our free A-level maths courses, studied in the second year of A-level. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. It sits alongside Second Derivatives & Stationary Points, Standard Functions, Tangents & Normals, Basic Differentiation and Chain Rule in the same strand. The Differentiation revision engine gives you as many extra questions as you want, tracked on your skill tree.
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