# Adjacent and the world of cosine

NOTE:

Only look at this if you want to know where cosine comes from.

Mathematicians built a world of right-angled triangles where the hypotenuse was always 1m long.

The mathematicians lifted a 1metre stick up in one degree intervals and measured how far the adjacent length along the floor was.

And for each degree they measured the length of the adjacent side of the triangle and plotted it on a graph. (The red triangle above shows the stick at 45 degrees, and the adjacent side is 0.707 metres along the floor.)

The length of the adjacent side for each degree increase is called the table/chart of cosine (angle) and is as follows:

NOTE:

Mathematicians can work this cosine curve above into a mathematical formula.

 Angle Adjacent distance (or cosine) 0^@ 1 \ metre 1^@ 0.99985 \ metres 2^@ 0.99939 \ metres 3^@ 0.99863 \ metres 4^@ 0.99756 \ metres 5^@ 0.99619 \ metres 6^@ 0.99452 \ metres 7^@ 0.99255 \ metres 8^@ 0.99027 \ metres 9^@ 0.98769 \ metres 10^@ 0.98481 \ metres 11^@ 0.98163 \ metres 12^@ 0.97815 \ metres 13^@ 0.97437 \ metres 14^@ 0.97030 \ metres 15^@ 0.96593 \ metres 16^@ 0.96126 \ metres 17^@ 0.95630 \ metres 18^@ 0.95106 \ metres 19^@ 0.94552 \ metres 20^@ 0.93969 \ metres 21^@ 0.93358 \ metres 22^@ 0.92718 \ metres 23^@ 0.92050 \ metres 24^@ 0.91355 \ metres 25^@ 0.90631 \ metres 26^@ 0.89879 \ metres 27^@ 0.89101 \ metres 28^@ 0.88295 \ metres 29^@ 0.87462 \ metres 30^@ 0.86603 \ metres 31^@ 0.85717 \ metres 32^@ 0.84805 \ metres 33^@ 0.83867 \ metres 34^@ 0.82904 \ metres 35^@ 0.81915 \ metres 36^@ 0.80901 \ metres 37^@ 0.79864 \ metres 38^@ 0.78801 \ metres 39^@ 0.77715 \ metres 40^@ 0.76604 \ metres 41^@ 0.75471 \ metres 42^@ 0.74314 \ metres 43^@ 0.73135 \ metres 44^@ 0.71934 \ metres 45^@ 0.70711 \ metres 46^@ 0.69466 \ metres 47^@ 0.68200 \ metres 48^@ 0.66913 \ metres 49^@ 0.65606 \ metres 50^@ 0.64279 \ metres 51^@ 0.62932 \ metres 52^@ 0.61566 \ metres 53^@ 0.60182 \ metres 54^@ 0.58779 \ metres 55^@ 0.57358 \ metres 56^@ 0.55919 \ metres 57^@ 0.54464 \ metres 58^@ 0.52992 \ metres 59^@ 0.51504 \ metres 60^@ 0.5 \ metres 61^@ 0.48481 \ metres 62^@ 0.46947 \ metres 63^@ 0.45399 \ metres 64^@ 0.43837 \ metres 65^@ 0.42262 \ metres 66^@ 0.40674 \ metres 67^@ 0.39073 \ metres 68^@ 0.37461 \ metres 69^@ 0.35837 \ metres 70^@ 0.34202 \ metres 71^@ 0.32557 \ metres 72^@ 0.30902 \ metres 73^@ 0.29237 \ metres 74^@ 0.27564 \ metres 75^@ 0.25882 \ metres 76^@ 0.24192 \ metres 77^@ 0.22495 \ metres 78^@ 0.20791 \ metres 79^@ 0.19081 \ metres 80^@ 0.17365 \ metres 81^@ 0.15643 \ metres 82^@ 0.13917 \ metres 83^@ 0.12187 \ metres 84^@ 0.10453 \ metres 85^@ 0.08716 \ metres 86^@ 0.06976 \ metres 87^@ 0.05234 \ metres 88^@ 0.03490 \ metres 89^@ 0.01745 \ metres 90^@ 0 \ metres