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 |