Using the Complex Expressions for Sine and Cosine.

ClearAll["Global`*"]
θ=30 (π/180); (* i.e., 30 degrees converted to radians*)
s1=Sin[θ];s2=(((E^(I θ))-(E^(-I θ)))/(2 I));
Print["Built in sine function is ",s1,", but complex expression is ",s2]
Print["  As decimals, these are ",1.0s1,",                       and ",1.0s2]

ClearAll["Global`*"]
θ=2.4 I ; (* 2.4I radians! *)
c1=Cos[θ];c2=(((E^(I θ))+(E^(-I θ)))/(2 ));
Print["Built in cosine function is ",c1,", but complex expression is ",c2]