log(1/2 i (e^(-i x) - e^(i x)))

x = 1/2 (4 π n + π), n element Z

{x element R : 0

{y element R : y<=0} (all non-positive real numbers)

log(x) - x^2/6 - x^4/180 + O(x^6) (generalized Puiseux series)

log(π - x) - 1/6 (x - π)^2 - 1/180 (x - π)^4 + O((x - π)^6) (generalized Puiseux series)

d/dx(log(sin(x))) = cot(x)

integral log(sin(x)) dx = 1/2 i (x^2 + Li_2(e^(2 i x))) - x log(1 - e^(2 i x)) + x log(sin(x)) + constant (assuming a complex-valued logarithm)

max{log(sin(x))} = 0 at x = 2 π n + π/2 for integer n

log(sin(x)) = log(e, sin(x))

log(sin(x)) = log(a) log(a, sin(x))

log(sin(x)) = log(cos(π/2 - x))

integral_0^π log(sin(x)) dx≈-2.177586090...

log(sin(x)) = - sum_(k=1)^∞ ((-1)^k (-1 + sin(x))^k)/k for abs(-1 + sin(x))<1

log(sin(x)) = log( sum_(k=0)^∞ ((-1)^k x^(1 + 2 k))/((1 + 2 k)!))

log(sin(x)) = log(-1 + sin(x)) - sum_(k=1)^∞ ((-1)^k (-1 + sin(x))^(-k))/k for abs(-1 + sin(x))>1

log(sin(x)) = integral_1^sin(x) 1/t dt

log(sin(x)) = log(x integral_0^1 cos(t x) dt)

log(sin(x)) = log(-(i x)/(4 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) e^(s - x^2/(4 s))/s^(3/2) ds) for γ>0