A Level Maths: Trigonometry: Secant, Cosecant and Cotangent Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
- Reciprocal Trig Functions and Compound Angles (OCR)
- Reciprocal Trig Functions and Compound Angles (Edexcel)
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Trigonometry — foundational identities and equations
- Trigonometry — Radians, Circle Sectors and Triangles}}: radian measure is standard
- Rational Expressions — useful for simplifying fractional expressions during identity proofs
A Level Maths trigonometry with secant, cosecant and cotangent introduces the three reciprocal trig functions: $\sec(x) = \frac{1}{\cos(x)}$, $\csc(x) = \frac{1}{\sin(x)}$, and $\cot(x) = \frac{1}{\tan(x)}$. You learn their graphs, key values, and the Pythagorean identities involving them, then use these to solve equations and prove identities — extending the toolkit from Trigonometry.
You meet the three reciprocal functions and their graphs, paying attention to their asymptotes (where the original trig function is zero, the reciprocal goes to infinity). You learn the extended Pythagorean identities derived from $\sin^2(x) + \cos^2(x) = 1$: dividing by $\cos^2(x)$ gives $\tan^2(x) + 1 = \sec^2(x)$, and dividing by $\sin^2(x)$ gives $1 + \cot^2(x) = \csc^2(x)$. You use these to solve equations involving the reciprocal functions, often by rewriting in terms of $\sin$ and $\cos$ to apply familiar techniques. You also prove identities involving the reciprocal functions, where the strategy is often to convert everything to $\sin$ and $\cos$, simplify, and convert back.
Trigonometry: secant, cosecant and cotangent is part of the Pure Maths strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: $\sec$, $\csc$, and $\cot$ are NOT the inverse trig functions — those are $\arcsin$, $\arccos$, $\arctan$, and they are completely different (see Trigonometry: Small Angle Approximations and Inverse Trig Functions); $\csc$ corresponds to $\sin$ (note the swap) and $\sec$ corresponds to $\cos$ — this is counter-intuitive; the asymptotes of $\sec(x)$ are where $\cos(x) = 0$, which is at $\pi/2 + n\pi$; and dividing the basic identity by $\cos^2$ introduces $\sec^2$, NOT $\csc^2$.