Geometry & measures · Pythagoras & right-angled trigonometry
Chapter 1 · 3
The idea
Exact trig values (sin, cos and tan of 0°, 30°, 45°, 60° and 90°)
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
Geometry & measures · Pythagoras & right-angled trigonometry
Exact trig values (sin, cos and tan of 0°, 30°, 45°, 60° and 90°)
Where the exact values of sin, cos and tan come from: two triangles you can sketch in seconds, half a square and half an equilateral triangle, plus a ladder lying flat or standing upright for 0° and 90°. How to use them to find an exact side in surd form, how to get an angle back from an exact ratio, and how to answer a non-calculator "show that" with exact values.
Why it works
The question a calculator can't answer
A ladder m long leans against a wall. It makes an angle of with the flat ground. How high up the wall does it reach?The wall is opposite the angle and the ladder is the hypotenuse, so the height is . A calculator says , and the digits never stop. A non-calculator paper wants the exact value: m. "Exact" means a whole number, a fraction or a surd, never a rounded decimal. By the end of this page you will reach with no calculator, from two triangles you can sketch in seconds. This ladder stays with us all the way through.Keep reading — free
The rest of the explanation, plus 4 worked examples you step through move by move.
Start freeTakes a minute — no card.