[VA] SRC#004- Fun with Sexagesimal Trigs

[Albert Chan]

Prove C = 1:

Using shorthand c(#) = c# = cos(#°), s(#) = s# = sin(#°)

C = (1 - c61/c1)(1 - c62/c2) ... (1 - c119/c59)

center = (1 + c90/c30) = (1 + 0/c30) = 1

Check the edges, each pair P had the form:
= (1 - c(90-x)/c(30-x)) * (1 - c(90+x)/c(30+x))
= (1 - sx / c(30-x)) * (1 + sx / c(30+x))

To simplify P, we need these identities:
cos(A+B) = cos(A)cos(B) − sin(A)sin(B)
cos(A−B) = cos(A)cos(B) + sin(A)sin(B)

Removing the annoying denominator, let k = c(30-x) * c(30+x)

k P
= (c(30+x) - sx) * (c(30-x) + sx)
= k + sx^2 + sx * (c(30+x) - c(30-x))
= k + sx^2 + sx * (-2 s(30) sx)
= k + sx^2 − sx^2
= k
-> P = 1

All factors can considered value of 1, thus C = 1