trig identities and equations

sin^2x+cos^2x

=1

cos^2x-sin^2x

=cos2x

1+cot^2x

=csc^2x

tan^2x+1

=sec^2x

sinx

=1/cscx

cosx

=1/secx

tanx

=1/cotx

cos(-x)

=cosx

sec(-x)

=secx

tan(-x) or -tanx

=sin(-x)/cos(-x)

even

cosx, secx

odd

sinx, cscx, tanx, cotx

sin(pi/2-x)

=cosx

cos(pi/2-x)

=sinx

tan(pi/2-x)

=cotx

csc(pi/2-x)

=secx

sec(pi/2-x)

=cscx

cot(pi/2-x)

=tanx

sin(u+v)

= sin(u)cos(v) + cos(u)sin(v)

sin(u-v)

= sin(u)cos(v)-cos(u)sin(v)

cos(u+v)

= cos(u)cos(v)-sin(u)sin(v)

cos(u-v)

= cos(u)cos(v) + sin(u)sin(v)

tan(u+v)

= tan(u)+tan(v)/1-tan(u)tan(v)

tan(u-v)

= tan(u)-tan(v)/1+tan(u)tan(v)

sin2(u)

= 2sin(u)cos(u)

tan2(u)

= 2tan(u)/1-tan(u)^2

cos2(u)

cos^2(u)-sin^2(u) OR 2cos^2(u)-1 OR 1-2sin^2(u)

θ

full angle

θ/2

half angle

The + or - depends on the __ in which θ/2 lies

quadrant

sin θ/2

± √ (1 - cosθ)/2

cos θ/2

± √(1 + cos θ)/2

tan θ/2

±√(1-cosθ)/(1+cosθ)