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Wasileski PreCalc

LCCC Mr. Wasileski Pre-Calc Final

Equation of a circle (x-h)^2+(y-k)^2=r^2
Center (h,k)
Distance Formula d=(|x2-x1|^2+|y2-y1|^2)1/2
Function A rule (or rules) which determines exactly one output number for any legitimate input number.
Point-slope Formula y-y1=m(x-x1)
Slope (y2-y1)/(x2-x1)
Slope Intercept Formula y=mx+b
Domain set of all input numbers
Range All possible output numbers
Parallel Line Slope m1=m2
Perpendicular Line Slope m2=-1/m1
Quadratic Function ax^2+bx+c or f(x)=a(x-h)^2+k, vertex=(x-h), h=b/2a, k=c
f(x-h)+k h= horizontal translation k= vertical translation
Quadratic Formula (-b+-(b^2-4ac)1/2)/2a
Odd Function f(-x)=-f(x)
Even Function f(-x)=f(x)
Vertical Asymptote =bottom/Domain
Horizontal Asymptote bottom=0
Finding Inverse Function replace f(x) with y, switch y and x, solve for y, that's inverse
Exponential Function f(x)=cb^x c=coefficient b=base
Exponential Models A(t)=Ao(1+(r/n))^nt A(t)=Aoe^rt
Log properties logb(mn) = logb(m) + logb(n)/ (logb(m/n) = logb(m) – logb(n)/ logb(m^n) = n · logb(m)/ logb1=0/ logb0=undefined/ logbx=logax/logab any a.
Degrees to Radians, Radians to Degrees Degrees(pi/180), Radians(180/pi)
Conversion between degrees and radians 360deg=2pi radians, 180deg=pi radians, 90deg=pi/2 radians, 45deg=pi/4 radians, 60deg=pi/3 radians
Sector S=rx
Circumference C=pi(d)
Area of Sector A=1/2r^2x
Trig. Ratios sinx=O/H, cosx=A/H, tanx=O/A, cotx=A/O, secx=H/A, cscx=H/O
Circle Trig. sinx=y/r, cosx=x/r, tanx=y/x, cotx=x/y, secx=r/x, cscx=r/y
Trig function graphs f(t)=asinb(t-c) |a|=amplitude period=2pi/b, tan period=pi/b phase shift=c
Trig Identities x^2+y^2=1, sin^2x+cos^2x=1, cos^2x+sin^2x=1, sin^2x=1-cos^2x, cos^2x=1-sin^2x, 1+tan^2x=sec^2x, 1+cot^2x=csc^2x
Trig Identities Cont. tanx=sinx/cosx, cotx=cosx/sinx, tan^px=sin^px/cos^px, sec^px=1/cos^px, csc^px=1/sin^px
Even more Trig Indentites sinx=1/cscx, cosx=1/secx, tanx=1/cotx, cscx=1/sinx, secx=1/cosx, cotx=1/tanx
Last of Trig Indentities sin(-x)=-sin(x), cos(-x)=cos(x), tan(-x)=-tan(x) csc(-x)=-csc(x) sec(-x)=sec(x), cot(-x)=-cot(x)
Law of Sines (sinA/a)=(sinB/b)=(sinC/c) ASA, AAS, SSA*
Law of Cosines a^2=b^2+c^2-2abcosA or cosA=(b^2+c^2-a^2)/(2bc)
Infinite Sequence an=1/2n+3 ex.
Arithmetic sequence an=dn+c
Geometric Sequence an=cr^(n-1)
Fibonacci Sequence an=a(n-2)-a(n-1) ex. 1,1,2,3,5,8,13,21,34,55,89
Created by: 14diltzd