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

The mathematicians lifted a 1 metre stick up in one degree intervals and measured how far the end lifted off the floor.

Fore each degree they measured the opposite side which changed slowly

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.)

Each measurement can be plotted on a graph, where a curve forms, this is the sine curve

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