半形公式

x/2

x

x

sin(1/2x)

=

(-1)^(|_x/(2pi)_|)sqrt((1-cosx)/2)

cos(1/2x)

=

(-1)^(|_(x+pi)/(2pi)_|)sqrt((1+cosx)/2)

tan(1/2x)

=

(-1)^(|_x/pi_|)sqrt((1-cosx)/(1+cosx))

=

(sinx)/(1+cosx)

=

(1-cosx)/(sinx)

=

(tanxsinx)/(tanx+sinx)

=

((-1)^(|_(x+pi/2)/pi_|)sqrt(1+tan^2x)-1)/(tanx).

sinh(1/2x)

=

sgn(x)sqrt((coshx-1)/2)

cosh(1/2x)

=

sqrt((coshx+1)/2)

tanh(1/2x)

=

(sinhx)/(coshx+1)

=

(coshx-1)/(sinhx).

cost

=

(1-tan^2(1/2t))/(1+tan^2(1/2t))

sint

=

(2tan(1/2t))/(1+tan^2(1/2t)).