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Wasileski PreCalc
LCCC Mr. Wasileski Pre-Calc Final
| Term | Definition |
|---|---|
| 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 |
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