top of page
This topic covers the trigonometric ratios sine, cosine and tangent, and the exact values for key angles (0°, 30°, 45°, 60°, 90°) that must be known without a calculator, in surd form. 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
Learn the exact values for 30, 45 and 60 degrees from the two standard triangles. Use them to answer without a calculator and to leave surd answers exact — decimals lose the accuracy marks.
Before you start
It draws heavily on right-angled trigonometry and surds. It is Pure 1 content. Getting it right here pays off in solving equations without a calculator.
What you learn
Beyond right-angled triangles, sinθ, cosθ and tanθ are defined for any angle. Two reference triangles give every special value. The sign of a ratio is simply whether its graph is above the θ -axis (positive) or below it (negative). Curve symmetry turns a special value into its partners. The course works through the special-angle exact values, signs from the graphs, exact values in every quadrant, symmetry and periodicity and solving in a range from the graph. 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
Trig Ratios & Exact Values is a Trigonometry topic in the A-level syllabus, covered here at the AS year. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. It sits alongside Addition Formulae, Double Angle Formulae, Further Trig Equations and Inverse Trig Functions in the same strand. The Trigonometry revision engine gives you as many extra questions as you want, tracked on your skill tree.
Still need help with a topic?
bottom of page