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# Precalculus Formulas

### formulas for precalc

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) |