Formulas from Geometry
A=area,A=area, V=Volume,andV=Volume,and S=lateral surface areaS=lateral surface area
Formulas from Algebra
Laws of Exponents
xmxn=xm+nxmxn=xm−n(xm)n=xmn x−n=1xn(xy)n=xnyn(xy)n=xnyn x1/n=xnxyn=xnynxyn=xnyn xm/n=xmn=(xn)mxmxn=xm+nxmxn=xm−n(xm)n=xmn x−n=1xn(xy)n=xnyn(xy)n=xnyn x1/n=xnxyn=xnynxyn=xnyn xm/n=xmn=(xn)m
Special Factorizations
x2−y2=(x+y)(x−y)x3+y3=(x+y)(x2−xy+y2)x3−y3=(x−y)(x2+xy+y2)x2−y2=(x+y)(x−y)x3+y3=(x+y)(x2−xy+y2)x3−y3=(x−y)(x2+xy+y2)
Quadratic Formula
If ax2+bx+c=0,ax2+bx+c=0, then x=−b±b2−4ac2a.x=−b±b2−4ac2a.
Binomial Theorem
(a+b)n=an+(n1)an−1b+(n2)an−2b2+⋯+(nn−1)abn−1+bn,(a+b)n=an+(n1)an−1b+(n2)an−2b2+⋯+(nn−1)abn−1+bn,
where (nk)=n(n−1)(n−2)⋯(n−k+1)k(k−1)(k−2)⋯3⋅2⋅1=n!k!(n−k)!(nk)=n(n−1)(n−2)⋯(n−k+1)k(k−1)(k−2)⋯3⋅2⋅1=n!k!(n−k)!
Formulas from Trigonometry
Right-Angle Trigonometry
sinθ=opphypcscθ=hypoppcosθ=adjhypsecθ=hypadjtanθ=oppadjcotθ=adjoppsinθ=opphypcscθ=hypoppcosθ=adjhypsecθ=hypadjtanθ=oppadjcotθ=adjopp
Trigonometric Functions of Important Angles
row: θθ | RadiansRadians | sinθsinθ | cosθcosθ | tanθtanθ
row: 0°0° | 00 | 00 | 11 | 00
row: 30°30° | π/6π/6 | 1/21/2 | 3/23/2 | 3/33/3
row: 45°45° | π/4π/4 | 2/22/2 | 2/22/2 | 11
row: 60°60° | π/3π/3 | 3/23/2 | 1/21/2 | 33
row: 90°90° | π/2π/2 | 11 | 00 | —
Fundamental Identities
sin2θ+cos2θ=1sin(−θ)=−sinθ 1+tan2θ=sec2θcos(−θ)=cosθ1+cot2θ=csc2θtan(−θ)=−tanθsin(π2−θ)=cosθsin(θ+2π)=sinθ cos(π2−θ)=sinθcos(θ+2π)=cosθ tan(π2−θ)=cotθtan(θ+π)=tanθsin2θ+cos2θ=1sin(−θ)=−sinθ 1+tan2θ=sec2θcos(−θ)=cosθ1+cot2θ=csc2θtan(−θ)=−tanθsin(π2−θ)=cosθsin(θ+2π)=sinθ cos(π2−θ)=sinθcos(θ+2π)=cosθ tan(π2−θ)=cotθtan(θ+π)=tanθ
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