Exact Trigonometric Values

What is Exact Trigonometric Values?

The values of sine, cosine and tangent at the special angles, written as whole numbers, fractions and surds rather than as decimals. Sine and cosine are known exactly at 0, 30, 45, 60 and 90 degrees, and tangent at 0, 30, 45 and 60 degrees; tangent is undefined at 90 degrees because the adjacent side there has shrunk to nothing. Every value can be rebuilt from two triangles: an equilateral triangle of side two cut in half, which yields the 30 and 60 degree values from sides of 1, root 3 and 2, and a right-angled isosceles triangle with two sides of 1, which yields the 45 degree values from a hypotenuse of root 2. Knowing them exactly is what allows a trigonometric calculation to be completed on a paper where no calculator is permitted.

This definition is part of the Trigonometry chapter in Cambridge IGCSE Mathematics.