trig final equations

cos(u-v)=

cos(u-v)=

cosucosv+sinusinv

cos(u+v)=

cosucosv-sinusinv

sin(u+v)=

sinucosv+cosusinv

sin(u-v)=

sinucosv-cosusinv

tan(u+v)=

tanu+tanv/1-tanutanv

tan(u-v)=

tanu-tanv/1+tanutanv

sin2u=

2sinucosu

cos2u=

cos^2u-sin^2u

cos2u=

1-2sin^2u

cos2u=

2cos^2u-1

tan2u=

2tanu/1-tan^2u

sin^2u=

1-cos2u/2

cos^2u=

1+cos2u/2

tan^2u

1-cos2u/1+cos2u

sinu/2=

+-sqrt(1-cosu/2)

cosu/2=

+-sqrt(1+cosu/2)

tanu/2=

+-sqrt(1-cosu/1+cosu)

sin-1:

Domain: [-1, 1], Range: [-pi/2, pi/2]

cos-1:

Domain: [-1,1], Range: [0,pi]

tan-1:

Domain: (-infinity, infinity), Range: (-pi/2, pi/2)

a^2=

b^2+c^2-2bccosA

At=

1/2bcsinA

Herron's: At=

sqrt(s)(s-a)(s-b)(s-c)

s=

1/2(a+b+c)

Parabola (up/down) formula

(x-h)^2=4p(y-k)

Parabola (sideways)

(y-k)^2=4p(x-h)

Ellipse (sideways) formula

(x-h)^2/a^2 + (y-k)^2/b^2=1

Ellipse (up/down) formula

(x-h)^2/b^2 + (y-k)^2/a^2=1

Hyperbola (sideways) formula

(x-h)^2/a^2 - (y-k)^2/b^2=1

Hyperbola (up/down) formula

(y-k)^2/a^2 - (x-h)^2/b^2=1

Complete the square

(b/2)^2

Non linear systems

substitution

Linear systems

substitution and elimination

arc length

s=theta(r)

Parabola (up/down) vertex

(h, k)

Parabola (up/down) focus

(h, k+p)

Parabola (up/down) directrix

y=k-p

Parabola (sideways) vertex:

(h, k)

Parabola (sideways) focus:

(h+p, k)

Parabola (sideways) directrix:

x=h-p

Ellipse abc

a^2-b^2=c^2

Ellipse (sideways) foci

(h+_c, k)

Ellipse (sideways) vertices

(h+-a, k)

Ellipse (sideways) MM1

(h, k+-b)

Ellipse (up/down) foci

(h, k+-c)

Ellipse (up/down) vertices

(h, k+-a)

Ellipse (up/down) MM1

(h+-b, k)

Hyperbolas abc

a^2+b^2=c^2

Hyperbola (sideways) foci

(h+-c, k)

Hyperbola (sideways) vertices

(h+-a, k)

Hyperbola (sideways) MM1

(h, k+-b)

Hyperbola (sideways) asymptotes

y=+-b/a (x-h)+k

Hyperbola (up/down) foci

(h, k+-c)

Hyperbola (up/down) vertices

(h, k+-a)

Hyperbola (up/down) MM1

(h+-b, k)

Hyperbola (up/down) asympptotes

y=+-a/b (x-h)+k

Area of circle

1/2r^2theta