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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.
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name
formula
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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