Precalculus Formulas Word Scramble
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name | formula |
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 |
converting degrees to radians | # degree * pi(radians)/180(degrees) |
converting radians to degrees | radians * 180(degrees)/pi(radians) |
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
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