Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# 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) |

Created by:
selfstudy08