formulas for precalc
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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exponential funtcion | f(x)=a^x
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natural exponential function | f(x)= e^x
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n compoundings per year | A=P(1+r/n)^(nt)
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continuous compounding | A=Pe^(rt)
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exponential growth model | y=ae^(bx), b>0
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exponential decay model | y=ae^(-bx), b>0
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Gaussian model | y=ae^(((-x-b)^2)/c), b>0
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logistic growth model | y=a/(1+be^(-rx))
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logarithmic model | y=a+b ln(x)
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logarithmic model | y=a+b log(x)
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length of a circular arc | s=r * theta(in radians)
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linear speed | arc length/time (s/t)
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angular speed | central angle/time (theta/t)
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sine function | sin t=y
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cosine function | cos t= x
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tangent function | tan t=y/x, x can't be 0
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cotangent function | cot t=x/y, y can't be 0
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cosecant function | csc t= 1/x, x can't be 0
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secant function | sec t=1/y, y can't be 0
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converting degrees to radians | # degree * pi(radians)/180(degrees)
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converting radians to degrees | radians * 180(degrees)/pi(radians)
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finding arc length | theta/360 * 2(pi)r
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heron's formula (triangle area) | sq rt(s*s-a*s-b*s-c)
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law of sines | a/sinA=b/sinB=c/sinC
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law of cosines (SSS,SAS) for side a | a^2 = b^2 + c^2 - 2bc(cos A)
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law of cosines (SSS,SAS) for side b | b^2 = a^2 + c^2 - 2ac(cos B)
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law of cosines f(SSS,SAS) or side c | c^2 = a^2 + b^2 - 2ab(cos C)
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law of cosines (SSS,SAS) for angle A | cos A = (b^2 + c^2 - a^2)/ 2bc
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law of cosines (SSS,SAS) for angle B | cos B = (a^2 + c^2 - b^2)/ 2ac
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law of cosines (SSS,SAS) for angle C | cos C = (a^2 + b^2 - c^2)/ 2ab
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area of a triangle | 1/2 cb sinA
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area of a triangle | 1/2 ac sinB
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area of a triangle | 1/2 ab sinC
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magnitude of v (vector) | II v II or I v I = II < a,b > = sq rt (a^2 + b^2)
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writing a vector sum as a linear combination | v1 i + v2 j
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writing vectors with direction angle(#) | v = II v II (cos #)i + II vII (sin #)j
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law of cosines (with vectors) | cos # = (U dot V ) / ( II U II II V II )
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dot products | <a1,a2> dot <b1,b2> = a1b1 + a2b2
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cos# = a/r (rewriting trig form of complex #s) | a = r cos#
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sin# = b/r (rewriting trig form of complex #s) | b = r sin#
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"modulous" | I a + bi I
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trig form of a complex # | r (cos# + i sin#)
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multiplying complex #s in trig form | z1z2 = r1r2 (cos(#+$) + i sin(#+$))
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dividing complex #s in trig form | z1/z2 = (r1/r2) (cos(# - $) + i sin(# - $)), z can be 0
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DeMoivre's Therom | z^n= r^n (cos(n#) + i sin(n#))
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nth roots of complex #s in trig form | n rt(z) =n rt(r) * (cos((#+2k*pi)/n) + i sin((#+2k*pi)/n))
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nth term of an arithmetic sequence | a(sub n)=a1 + d(n-1)
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sum of a finite arithmetic sequence | Sn=(n/2)*(a1+a(sub n))
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partial sum of an aritmetic sequence | Sn=(n/2)*(a1+a(sub n))
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sum of a finite geometric sequence | Sn=(a1)*((1-r^n)/(1-r))
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sum of an infinite geometric sequence | S=(a1)/(1-r)
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increasing annuity | A=P((1+r/12)^n)
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Created by:
selfstudy08
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