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

x = π n, n element Z

x = 0

R (all real numbers)

{y element R : -1<=y<=1}

periodic in x with period 2 π

odd

x - x^3/6 + x^5/120 + O(x^6) (Taylor series)

d/dx(sin(x)) = cos(x)

integral sin(x) dx = -cos(x) + constant

sin(x) = -i sinh(π - i x)

sin(x) = i sinh(π + i x)

sin(x) = i sinh(2 π - i x)

sin(x) = -i sinh(2 π + i x)

sin(x) = 3 sin(x/3) - 4 sin^3(x/3)

sin(x) = 2 cos(x/2) sin(x/2)

sin(x) = i (-1)^m sinh(m π - i x) for m element Z

sin(x) = 1/2 sec(b) (-sin(b - x) + sin(b + x))

min{sin(x)} = -1 at x = 2 π n - π/2 for integer n

min{sin(x)} = -1 at x = 2 π n + (3 π)/2 for integer n

max{sin(x)} = 1 at x = 2 π n + π/2 for integer n

sin(x) = 1/csc(x)

sin(x) = cos(π/2 - x)

sin(x) = -cos(π/2 + x)

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

sin(x)∝( sum_(k=0)^∞ (-1)^k (d^(2 k) δ(x))/(dx^(2 k)))/θ(x)

sin(x) = 2 sum_(k=0)^∞ (-1)^k J_(1 + 2 k)(x)

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

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

sin(x) = -i/(2 sqrt(π)) integral_(-i ∞ + γ)^(i ∞ + γ) (2^(-1 + 2 s) x^(1 - 2 s) Γ(s))/Γ(3/2 - s) ds for (0<γ<1 and x>0)

integral_0^π sin(x) dx = 2

integral_0^(2 π) (sin^2(x))/(2 π) dx = 1/2 = 0.5