top of page
Radians are the natural angle measure where 2π radians = 360°. This topic converts between degrees and radians and uses arc length = rθ and sector area = ½r²θ to solve problems with sectors and segments. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Arc length is r times theta and sector area is half r squared theta, with the angle in radians. Convert degrees by multiplying by pi over 180. Using degrees in these formulas is the usual slip — the calculator must be in radian mode too.
Before you start
The prerequisite is circle measure and degrees. It leads on to calculus with trigonometric functions. This sits in Pure 1.
What you learn
One radian is the angle subtended at the centre by an arc whose length equals the radius. Exam questions often give you the arc or the area and ask for the radius or the angle. A segment is the region between a chord and its arc. The course works through radian measure, arc length and sector area, working backwards to r or θ, segments, composite figures and applied problems. 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
In our A-level maths courses, Radians, Arcs & Sectors belongs to Trigonometry and is met in the AS year. You work through 6 concepts and 6 worked examples, testing yourself at 6 points. Related topics students usually take next include Reciprocal Trig Functions, Sine & Cosine Rules, Solving Trig Equations, Trig Graphs & Transformations and Trig Identities (C12). Endless extra practice on this strand is available on the Trigonometry revision engine, which generates a fresh question each time.
Still need help with a topic?
bottom of page