微積分常用公式總結(一)

04-19

高等數學基礎

函數

數列

三角函數

$sin^2alpha + cos^2alpha = 1$ $sec^2alpha - tan^2alpha = 1$ $csc^2alpha - cot^2alpha = 1$
$sin2alpha = 2sinalpha cosalpha$ $cos2alpha = 2cos^2alpha - 1 = 1 - sin^2alpha = cos^2alpha - sin^2alpha$
$sin3alpha = -4sin^3alpha + 3sinalpha$ $cos3alpha = 4cos^3alpha-3cosalpha$
$sin^2alpha = (1-cos2alpha)/2$ $cos^2alpha = (1+cos2alpha)/2$
$tan2alpha = 2tanalpha/(1-tan^2alpha)$ $cos2alpha = (cot^2alpha-1)/2cotalpha$
$tanalpha/2=(1-cosalpha)/sinalpha = sinalpha/(1+cosalpha)$ $cotalpha/2 = sinalpha/(1-cosalpha)=(1+cosalpha)/sinalpha$
$sin(alpha+-eta)=sinalpha coseta+-cosalpha sineta$ $cos(alpha+-eta)=cosalpha coseta-+sinalpha sineta$ $tan(alpha+-eta)=(tanalpha+-taneta)/(1-+tanalpha taneta)$ $cot(alpha+-eta)=(cotalpha coteta-+1)/(coteta+-cotalpha)$
$sinalpha coseta = [sin(alpha+eta)+sin(alpha-eta)]/2$ $cosalpha coseta = [cos(alpha+eta)+cos(alpha-eta)]/2$ $sinalpha sineta = [cos(alpha-eta)-cos(alpha+eta)]/2$
$sinalpha+sineta = 2sin[(alpha+eta)/2]cos[(alpha-eta)/2]$ $sinalpha-sineta=2sin[(alpha-eta)/2]cos[(alpha+eta)/2]$ $cosalpha+coseta=2cos[(alpha+eta)/2]cos[(alpha-eta)/2]$ $cosalpha-coseta=-2sin[(alpha+eta)/2]sin[(alpha-eta)/2]$

階乘