Exact trigonometric values

In mathematics, the values of the trigonometric functions can be expressed approximately, as in ${\displaystyle \cos(\pi /4)\approx 0.707}$, or exactly, as in ${\displaystyle \cos(\pi /4)={\sqrt {2}}/2}$. While trigonometric tables contain many approximate values, the exact values for certain angles can be expressed by a combination of arithmetic operations and square roots. The angles with trigonometric values that are expressible in this way are exactly those that can be constructed with a compass and straight edge, and the values are called constructible numbers.