PreCalc Final Formulas Flashcards
Midpoint of a segment
(X1+x2)/2 , (y1+y2)/2
Circle Formula
(x-h)^2 +(y-k)^2 = r^2
Equations of Lines
y=mx+b
y1-y2= m(x-x1) -point slope form
Function rules:
-Finding the domain
if it’s a square root, set radicand >or= 0
If it’s a fraction, set denom = 0
If it’s a root in the denom, set radicand > 0
Square root over a denom, set rad >or= 0 & set denom = 0
Even or Odd
If f(-x) = f(x) EVEN If f(-x) = -f(x) ODD
-Could also be neither
Symmetry:
X-axis
Y-axis
Origin
(x,y) and (x,-y) appear on the graph
“ and (-x,y) appear on the graph
“ and (-x,-y) appear on the graph
Inverse
Switch the x and the y
Solve for y
Variations
y varies jointly as x: y=kx
y varies inversely as x: y=k/x or xy=k
y varies jointly as x and z: y=kxz
Parabolas
f(x) = a(x-h)^2 + k
When V(h,k)
Leading Coefficient Test
⬆️⬆️ 3x^4 ⬆️⬇️-5x^3
⬇️⬇️ -2x^2 ⬇️⬆️ 3x^5
Find vertical asymptotes by:
Setting the denom = 0
Horizontal asymptotes:
Degree of num > denom, HA is at y=0
Degree of num = denom, HA:y=leading coeff
Degree of num
Interest Formulas:
- —-Compoundings
- —-Continuously
- – A = P(1+ r/n)^nt
- – A = Pe^rt
Logarithms definition:
LOGb (a•c) =
LOGb (a/c) =
LOBb a^c =
LOGbX= y, so b^y=x
Change of Base Formula
LOGbA= LOGa/LOGb
To convert radians to degrees:
x 180/pi
sin-
cos-
tan-
csc
sec
cot
Pythagorean Identities:
sin^2θ+cos^2θ= 1
tan^2θ+1= sec^2θ
cot “ = csc^2θ
Cosine / Sine formula
y = a sin (bx + c) |a| = amplitude Period = 2pi/b
Tangent
y = tan x
Period = pi/b
Asymptotes: +- 1/2 period
Inverse Trig functions
Quadrants: tan & sin => I , IV
+ -
cos => I , II
+ -
Sum and Difference Formulas
sin (A + B)
sin (A - B)
cos (A+B)
cos (A-B)
sinAcosA + cosBsinB
sinAcosA - cosBsinB
cosAcosB - sinAsinB
cosAcosB + sinAsinB
Double Angles
sin 2θ
cos 2θ
sin 2θ: 2sinθcosθ
cos 2θ: cos^2θ - sin^2θ
1 - 2sin^2θ
2cos^2θ - 1
Trigonometric Form
•formula
•r=
•tanθ=
r(cosθ+i sinθ)
r= √ a^2 + b^2
tanθ= b/a
finding the Nth roots
nth root of r • [cos {(θ+360•n)/n} + i sin { } ]
K= 0,1,2,….,.n-1
Distance btwn two points
_____________________
d= √ (x1-x2)^2 + (y1-y2)^2
Arithmetic:
Nth term: An=
Sum of n terms=
An= a1 + (n-1)d Sn= n/2 (a1+an)
Geometric:
An=
Sn=
S∞=
An= a1•r^(n-1)
Sn= {a1(1-r^n)} / 1-r
S∞= a1/1-rCofunctions
sinθ=cos(90-θ)
tan “ cot
cos “ sec
Special Angles
30
45
60
pi/6
pi/4
pi/3
