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Computer Science · Data Sheet

Trigonometry, Matrices and Geometry Cheat Sheet

SymbolConstantValueUnit
c^2Pythagorean theoremc^2=a^2+b^2formula
sin(theta)Sinesin(theta)=opposite/hypotenuseformula
cos(theta)Cosinecos(theta)=adjacent/hypotenuseformula
tan(theta)Tangenttan(theta)=sin(theta)/cos(theta)formula
sin^2+cos^2Pythagorean identitysin(theta)^2+cos(theta)^2=1formula
1+tan^2Tangent identity1+tan(theta)^2=sec(theta)^2formula
sin(x+y)Sine additionsin(x+y)=sin(x)cos(y)+cos(x)sin(y)formula
cos(x+y)Cosine additioncos(x+y)=cos(x)cos(y)-sin(x)sin(y)formula
sin(2x)Double-angle sinesin(2x)=2sin(x)cos(x)formula
cos(2x)Double-angle cosinecos(2x)=cos(x)^2-sin(x)^2formula
exp(ix)Euler formulaexp(ix)=cos(x)+i sin(x)formula
exp(i*pi)Euler identityexp(i*pi)=-1formula
C=ABMatrix productc_ij=sum(k=1..n) a_ik*b_kjformula
det(AB)Determinant productdet(AB)=det(A)det(B)formula
det([[a,b],[c,d]])2x2 determinantdet=ad-bcformula
c^2Law of cosinesc^2=a^2+b^2-2ab cos(C)formula
ATriangle areaA=h*c/2formula
ATriangle sine areaA=a*b*sin(C)/2formula
AHeron formulaA=sqrt(s(s-a)(s-b)(s-c)), s=(a+b+c)/2formula
ACircle areaA=pi*r^2formula
VSphere volumeV=4*pi*r^3/3formula
dEuclidean distanced=sqrt((x1-x0)^2+(y1-y0)^2)formula
d_pLp distanced_p=(|x1-x0|^p+|y1-y0|^p)^(1/p)formula
ATriangle coordinate areaA=abs((x1-x0)(y2-y0)-(x2-x0)(y1-y0))/2formula

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A searchable formula reference transcribed and normalized from the supplied Theoretical Computer Science Cheat Sheet.

Trigonometry, Matrices and Geometry formula reference

This searchable reference organizes formulas from the supplied Theoretical Computer Science Cheat Sheet into web-friendly notation. Use the search box to find a formula by name or symbol, then review its assumptions before applying it.

Some identities use conventional mathematical notation such as summation limits, factorials, congruences, expectations and asymptotic bounds. These entries are reference material and should be interpreted within their stated domains.