Formulas from Geometry
A=area,V=Volume, and S=lateral surface area


Formulas from Algebra
Laws of Exponents
xmxnx−nx1/nxm/n====xm+nxn1nxnxm=(nx)mxnxm(xy)nnxy===xm−nxnynnxny(xm)n(yx)nnyx===xmnynxnnynx
Special Factorizations
x2−y2x3+y3x3−y3===(x+y)(x−y)(x+y)(x2−xy+y2)(x−y)(x2+xy+y2)
Quadratic Formula
If ax2+bx+c=0, then x=2a−b±b2−4ca.
Binomial Theorem
(a+b)n=an+(n1)an−1b+(n2)an−2b2+⋯+(nn−1)abn−1+bn,
where (nk)=k(k−1)(k−2)⋯3⋅2⋅1n(n−1)(n−2)⋯(n−k+1)=k!(n−k)!n!
Formulas from Trigonometry
Right-Angle Trigonometry
sinθ=hypoppcosθ=hypadjtanθ=adjoppcscθ=opphypsecθ=adjhypcotθ=oppadj

Trigonometric Functions of Important Angles
θ | Radians | sinθ | cosθ | tanθ |
0° | 0 | 0 | 1 | 0 |
30° | π/6 | 1/2 | 3/2 | 3/3 |
45° | π/4 | 2/2 | 2/2 | 1 |
60° | π/3 | 3/2 | 1/2 | 3 |
90° | π/2 | 1 | 0 | — |
Fundamental Identities
sin2θ+cos2θ1+tan2θ1+cot2θsin(2π−θ)cos(2π−θ)tan(2π−θ)======1sec2θcsc2θcosθsinθcotθsin(−θ)cos(−θ)tan(−θ)sin(θ+2π)cos(θ+2π)tan(θ+π)======−sinθcosθ−tanθsinθcosθtanθ
Law of Sines
asinA=bsinB=csinC

Law of Cosines
a2b2c2===b2+c2−2bccosAa2+c2−2accosBa2+b2−2abcosC
Addition and Subtraction Formulas
sin(x+y)sin(x−y)cos(x+y)cos(x−y)tan(x+y)tan(x−y)======sinxcosy+cosxsinysinxcosy−cosxsinycosxcosy−sinxsinycosxcosy+sinxsiny1−tanxtanytanx+tany1+tanxtanytanx−tany
Double-Angle Formulas
sin2xcos2xtan2x===2sinxcosxcos2x−sin2x=2cos2x−1=1−2sin2x1−tan2x2tanx
Half-Angle Formulas
sin2xcos2x==21−cos2x21+cos2x