A Level Maths: Trigonometry: Radians, Circle Sectors and Triangles 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.
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 trigonometry in degrees
- Circle Geometry — connects to sector and segment geometry
- Surds — needed for handling exact radian values
A Level Maths trigonometry with radians, circle sectors and triangles introduces radian measure — the natural unit for angles in calculus. Radians make many formulas much simpler than degrees, especially for arc length, sector area, and differentiation of trig functions. Mastering this early makes the rest of Year 2 trigonometry and calculus far easier.
A radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. The full circle is $2\pi$ radians $= 360^\circ$, so $1$ radian is approximately $57.3^\circ$. You convert between degrees and radians fluently. In radians, arc length is $s = r\theta$ and sector area is $A = \tfrac{1}{2}r^2\theta$ — both formulas only work with $\theta$ in radians. You know exact values of $\sin$ and $\cos$ at standard radian angles ($0$, $\pi/6$, $\pi/4$, $\pi/3$, $\pi/2$ and multiples), and use radian measure for all subsequent trig identities and equations. The exact values of $\tan(0)$, $\tan(\pi/6)$, $\tan(\pi/4)$, $\tan(\pi/3)$ and multiples are also expected.
Trigonometry: radians, circle sectors and triangles 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: the formulas $s = r\theta$ and $A = \tfrac{1}{2}r^2\theta$ REQUIRE $\theta$ in radians — applying them with degrees gives wrong answers; switch your calculator to radian mode for radian work, and DEGREE mode for degree work — getting this wrong is a classic exam slip; $\pi/4$ is $45^\circ$, $\pi/6$ is $30^\circ$, $\pi/3$ is $60^\circ$ — memorise these conversions; and area of a SEGMENT is not the same as area of a SECTOR — segment area requires subtracting a triangle.