Exact trigonometric values

Use exact values for the special angles. Half of an equilateral triangle of side 2 gives the 30 and 60 ratios. A right-angled isosceles triangle with legs 1 gives the 45 ratios. **Ratio** | **30 / pi6** | **45 / pi4** | **60 / pi3** sintheta | 12 | 1sqrt(2) | sqrt(3)2 costheta | sqrt(3)2 | 1sqrt(2) | 12 tantheta | 1sqrt(3) | 1 | sqrt(3) Values on the axes **Ratio** | **0 / 0** | **90 / pi2** | **180 / pi** | **270 / 3pi2** | **360 / 2pi** sintheta | 0 | 1 | 0 | -1 | 0 costheta | 1 | 0 | -1 | 0 | 1 tantheta | 0 | undefined | 0 | undefined | 0 Choose signs using the quadrant; a positive square has two possible square roots.