Pure · Trigonometry
Chapter 1 · 3
The idea
Exact values of trigonometric ratios
The exact surd values of sin, cos and tan at 0, 30, 45, 60 and 90 degrees, where they come from (two special triangles plus the unit circle), the sine ladder that rebuilds the whole table, and how to answer "find the exact value" questions without a calculator.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Pure · Trigonometry
Exact values of trigonometric ratios
The exact surd values of sin, cos and tan at 0, 30, 45, 60 and 90 degrees, where they come from (two special triangles plus the unit circle), the sine ladder that rebuilds the whole table, and how to answer "find the exact value" questions without a calculator.
Why it works
The question a calculator can't answer
Paper 1 is the non-calculator paper, and it loves to open with something like this: *find the exact value of , giving your answer as a single fraction.* Even with a calculator smuggled in, would score nothing — exact means fractions and surds, with no rounding anywhere. The good news is that every exact value the course expects falls out of just two triangles you can draw in the margin, plus a glance at the unit circle. Build them once and the whole table follows — and at the end of the lesson we'll come back and finish this exact question.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
Start freeTakes a minute — no card.