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 |



