Opposites and the world of sine
NOTE:
Only look at this if you want to know where sine comes from.
Mathematicians built a world of right-angled triangles where the hypotenuse was always 1m long.
The mathematicians lifted a 1 metre stick up in one degree intervals and measured how far the end lifted off the floor.
For each degree they also measured the length of the opposite side of the triangle and plotted it on a graph. (The red triangle above shows the stick at 45 degrees and the end of the stick (the opposite side) is 0.707 metres off the floor.)
The length of the opposite side for each degree increase is called the table/chart of sine (angle) and is as follows:
NOTE:
Mathematicians can work this sine curve above into a mathematical formula.
| Angle | Opposite distance (or sine) | |
| `0^@` | `0 \ metres` | |
| `1^@` | `0.01745 \ metres` | |
| `2^@` | `0.03490 \ metres` | |
| `3^@` | `0.05234 \ metres` | |
| `4^@` | `0.06976 \ metres` | |
| `5^@` | `0.08716 \ metres` | |
| `6^@` | `0.10453 \ metres` | |
| `7^@` | `0.12187 \ metres` | |
| `8^@` | `0.13917 \ metres` | |
| `9^@` | `0.15643 \ metres` | |
| `10^@` | `0.17365 \ metres` | |
| `11^@` | `0.19081 \ metres` | |
| `12^@` | `0.20791 \ metres` | |
| `13^@` | `0.22495 \ metres` | |
| `14^@` | `0.24192 \ metres` | |
| `15^@` | `0.25882 \ metres` | |
| `16^@` | `0.27564 \ metres` | |
| `17^@` | `0.29237 \ metres` | |
| `18^@` | `0.30902 \ metres` | |
| `19^@` | `0.32557 \ metres` | |
| `20^@` | `0.34202 \ metres` | |
| `21^@` | `0.35837 \ metres` | |
| `22^@` | `0.37461 \ metres` | |
| `23^@` | `0.39073 \ metres` | |
| `24^@` | `0.40674 \ metres` | |
| `25^@` | `0.42262 \ metres` | |
| `26^@` | `0.43837 \ metres` | |
| `27^@` | `0.45399 \ metres` | |
| `28^@` | `0.46947 \ metres` | |
| `29^@` | `0.48481 \ metres` | |
| `30^@` | `0.5 \ metres` | |
| `31^@` | `0.51504 \ metres` | |
| `32^@` | `0.52992 \ metres` | |
| `33^@` | `0.54464 \ metres` | |
| `34^@` | `0.55919 \ metres` | |
| `35^@` | `0.57358 \ metres` | |
| `36^@` | `0.58779 \ metres` | |
| `37^@` | `0.60182 \ metres` | |
| `38^@` | `0.61566 \ metres` | |
| `39^@` | `0.62932 \ metres` | |
| `40^@` | `0.64279 \ metres` | |
| `41^@` | `0.65606 \ metres` | |
| `42^@` | `0.66913 \ metres` | |
| `43^@` | `0.68200 \ metres` | |
| `44^@` | `0.69466 \ metres` | |
| `45^@` | `0.70711 \ metres` | |
| `46^@` | `0.71934 \ metres` | |
| `47^@` | `0.73135 \ metres` | |
| `48^@` | `0.74314 \ metres` | |
| `49^@` | `0.75471 \ metres` | |
| `50^@` | `0.76604 \ metres` | |
| `51^@` | `0.77715 \ metres` | |
| `52^@` | `0.78801 \ metres` | |
| `53^@` | `0.79864 \ metres` | |
| `54^@` | `0.80901 \ metres` | |
| `55^@` | `0.81915 \ metres` | |
| `56^@` | `0.82904 \ metres` | |
| `57^@` | `0.83867 \ metres` | |
| `58^@` | `0.84805 \ metres` | |
| `59^@` | `0.85717 \ metres` | |
| `60^@` | `0.86603 \ metres` | |
| `61^@` | `0.87462 \ metres` | |
| `62^@` | `0.88295 \ metres` | |
| `63^@` | `0.89101 \ metres` | |
| `64^@` | `0.89879 \ metres` | |
| `65^@` | `0.90631 \ metres` | |
| `66^@` | `0.91355 \ metres` | |
| `67^@` | `0.92050 \ metres` | |
| `68^@` | `0.92718 \ metres` | |
| `69^@` | `0.93358 \ metres` | |
| `70^@` | `0.93969 \ metres` | |
| `71^@` | `0.94552 \ metres` | |
| `72^@` | `0.95106 \ metres` | |
| `73^@` | `0.95630 \ metres` | |
| `74^@` | `0.96126 \ metres` | |
| `75^@` | `0.96593 \ metres` | |
| `76^@` | `0.97030 \ metres` | |
| `77^@` | `0.97437 \ metres` | |
| `78^@` | `0.97815 \ metres` | |
| `79^@` | `0.98163 \ metres` | |
| `80^@` | `0.98481 \ metres` | |
| `81^@` | `0.98769 \ metres` | |
| `82^@` | `0.99027 \ metres` | |
| `83^@` | `0.99255 \ metres` | |
| `84^@` | `0.99452 \ metres` | |
| `85^@` | `0.99619 \ metres` | |
| `86^@` | `0.99756 \ metres` | |
| `87^@` | `0.99863 \ metres` | |
| `88^@` | `0.99939 \ metres` | |
| `89^@` | `0.99985 \ metres` | |
| `90^@` | `1 \ metre` |
