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tan 165/2 = 1.068691
sin 480° is equal to sin 60°, which is sqrt(3)/2 or approximately 0.866.
tan x = sin x / cos x sin x = x - (x^3/3!) + (x^5/5!) - (x^7/7!) + (x^9/9!) ... to infinity cos x = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) + (x^8/8!) .. to infinity tan 165 degrees = -0.267949192
The numeric value is 165.
mostly it comes from memorization. If sin 30 = 1/2, then arcsin (1/2) = 30