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# Precalculus Formulas

### formulas for precalc

nameformula
exponential funtcion f(x)=a^x
natural exponential function f(x)= e^x
n compoundings per year A=P(1+r/n)^(nt)
continuous compounding A=Pe^(rt)
exponential growth model y=ae^(bx), b>0
exponential decay model y=ae^(-bx), b>0
Gaussian model y=ae^(((-x-b)^2)/c), b>0
logistic growth model y=a/(1+be^(-rx))
logarithmic model y=a+b ln(x)
logarithmic model y=a+b log(x)
length of a circular arc s=r * theta(in radians)
linear speed arc length/time (s/t)
angular speed central angle/time (theta/t)
sine function sin t=y
cosine function cos t= x
tangent function tan t=y/x, x can't be 0
cotangent function cot t=x/y, y can't be 0
cosecant function csc t= 1/x, x can't be 0
secant function sec t=1/y, y can't be 0
finding arc length theta/360 * 2(pi)r
heron's formula (triangle area) sq rt(s*s-a*s-b*s-c)
law of sines a/sinA=b/sinB=c/sinC
law of cosines (SSS,SAS) for side a a^2 = b^2 + c^2 - 2bc(cos A)
law of cosines (SSS,SAS) for side b b^2 = a^2 + c^2 - 2ac(cos B)
law of cosines f(SSS,SAS) or side c c^2 = a^2 + b^2 - 2ab(cos C)
law of cosines (SSS,SAS) for angle A cos A = (b^2 + c^2 - a^2)/ 2bc
law of cosines (SSS,SAS) for angle B cos B = (a^2 + c^2 - b^2)/ 2ac
law of cosines (SSS,SAS) for angle C cos C = (a^2 + b^2 - c^2)/ 2ab
area of a triangle 1/2 cb sinA
area of a triangle 1/2 ac sinB
area of a triangle 1/2 ab sinC
magnitude of v (vector) II v II or I v I = II < a,b > = sq rt (a^2 + b^2)
writing a vector sum as a linear combination v1 i + v2 j
writing vectors with direction angle(#) v = II v II (cos #)i + II vII (sin #)j
law of cosines (with vectors) cos # = (U dot V ) / ( II U II II V II )
dot products <a1,a2> dot <b1,b2> = a1b1 + a2b2
cos# = a/r (rewriting trig form of complex #s) a = r cos#
sin# = b/r (rewriting trig form of complex #s) b = r sin#
"modulous" I a + bi I
trig form of a complex # r (cos# + i sin#)
multiplying complex #s in trig form z1z2 = r1r2 (cos(#+\$) + i sin(#+\$))
dividing complex #s in trig form z1/z2 = (r1/r2) (cos(# - \$) + i sin(# - \$)), z can be 0
DeMoivre's Therom z^n= r^n (cos(n#) + i sin(n#))
nth roots of complex #s in trig form n rt(z) =n rt(r) * (cos((#+2k*pi)/n) + i sin((#+2k*pi)/n))
nth term of an arithmetic sequence a(sub n)=a1 + d(n-1)
sum of a finite arithmetic sequence Sn=(n/2)*(a1+a(sub n))
partial sum of an aritmetic sequence Sn=(n/2)*(a1+a(sub n))
sum of a finite geometric sequence Sn=(a1)*((1-r^n)/(1-r))
sum of an infinite geometric sequence S=(a1)/(1-r)
increasing annuity A=P((1+r/12)^n)
Created by: selfstudy08