Trigonometric Identities

Memorize the trigonometric identities!

csc(x)

=1/sin(x)

sec(x)

=1/cos(x)

cot(x)

=1/tan(x)

tan(x)

=sin(x)/cos(x)

cot(x)

=cos(x)/sin(x)

sin^2(x)+cos^2(x)

=1

tan²(x)+1

=sec²(x)

1+cot^2(x)

=csc^2(x)

sin(-x)

=-sin(x)

cos(-x)

=cos(x)

tan(-x)

=-tan(x)

csc(-x)

=-csc(x)

sec(-x)

=sec(x)

cot(-x)

=-cot(x)

sin((pi/2)-u)

=cos(u)

cos((pi/2)-u)

=sin(u)

tan((pi/2)-u)

=cot(u)

sin(x+y)

=sin(x)cos(y)+cos(x)sin(y)

sin(x-y)

=sin(x)cos(y)-cos(x)sin(y)

cos(x+y)

=cos(x)cos(y)-sin(x)sin(y)

cos(x-y)

=cos(x)cos(y)+sin(x)sin(y)

tan(x+y)

=(tan(x)+tan(y))/(1-tan(x)tan(y))

tan(x-y)

=(tan(x)-tan(y))/(1+tan(x)tan(y))

sin(2x)

=2sin(x)cos(x)

cos(2x)

=cos^2(x)-sin^2(x), 1-sin^2(x), 2cos^2(x)-1

tan(2x)

=(2tan(x))/(1-tan²(x))

sin(u/2)

=sqrt((1-cos(u))/2)

cos(u/2)

=sqrt((1+cos(u))/2)

tan(u/2)

=(1-cos(u))/sin(u)

=sin(u)/1+cos(u)

d/dx(sin(x))

=cos(x)

d/dx(cos(x))

=-sin(x)

d/dx(tan(x))

=sec²(x)

d/dx(csc(x))

=-csc(x)cot(x)

d/dx(sec(x))

=sec(x)tan(x)

d/dx(cot(x))

=-csc²(x)