PreCalc Final Formulas

Question 1

Midpoint of a segment

Answer 1

(X1+x2)/2 , (y1+y2)/2

Question 2

Circle Formula

Answer 2

(x-h)^2 +(y-k)^2 = r^2

Question 3

Equations of Lines

Answer 3

y=mx+b

y1-y2= m(x-x1) -point slope form

Question 4

Function rules:

-Finding the domain

Answer 4

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

Question 5

Even or Odd

Answer 5

If f(-x) = f(x)     EVEN
If f(-x) = -f(x)     ODD

-Could also be neither

Question 6

Symmetry:
X-axis
Y-axis
Origin

Answer 6

(x,y) and (x,-y) appear on the graph
“ and (-x,y) appear on the graph
“ and (-x,-y) appear on the graph

Question 7

Inverse

Answer 7

Switch the x and the y

Solve for y

Question 8

Variations

Answer 8

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

Question 9

Parabolas

Answer 9

f(x) = a(x-h)^2 + k

When V(h,k)

Question 10

Leading Coefficient Test

Answer 10

⬆️⬆️ 3x^4 ⬆️⬇️-5x^3

⬇️⬇️ -2x^2 ⬇️⬆️ 3x^5

Question 11

Find vertical asymptotes by:

Answer 11

Setting the denom = 0

Question 12

Horizontal asymptotes:

Answer 12

Degree of num > denom, HA is at y=0
Degree of num = denom, HA:y=leading coeff
Degree of num

Question 13

Interest Formulas:

• —-Compoundings
• —-Continuously

Answer 13

• – A = P(1+ r/n)^nt

- – A = Pe^rt

Question 14

Logarithms definition:
LOGb (a•c) =
LOGb (a/c) =
LOBb a^c =

Answer 14

LOGbX= y, so b^y=x

Question 15

Change of Base Formula

Answer 15

LOGbA= LOGa/LOGb

Question 16

To convert radians to degrees:

Answer 16

x 180/pi

Question 17

sin-
cos-
tan-

Answer 17

csc
sec
cot

Question 18

Pythagorean Identities:

Answer 18

sin^2θ+cos^2θ= 1
tan^2θ+1= sec^2θ
cot “ = csc^2θ

Question 19

Cosine / Sine formula

Answer 19

y = a sin (bx + c)
|a| = amplitude
Period = 2pi/b

Question 20

Tangent

Answer 20

y = tan x
Period = pi/b
Asymptotes: +- 1/2 period

Question 21

Inverse Trig functions

Answer 21

Quadrants: tan & sin => I , IV
+ -
cos => I , II
+ -

Question 22

Sum and Difference Formulas
sin (A + B)
sin (A - B)

cos (A+B)
cos (A-B)

Answer 22

sinAcosA + cosBsinB
sinAcosA - cosBsinB

cosAcosB - sinAsinB
cosAcosB + sinAsinB

Question 23

Double Angles
sin 2θ
cos 2θ

Answer 23

sin 2θ: 2sinθcosθ

cos 2θ: cos^2θ - sin^2θ
1 - 2sin^2θ
2cos^2θ - 1

Question 24

Trigonometric Form
•formula
•r=
•tanθ=

Answer 24

r(cosθ+i sinθ)
r= √ a^2 + b^2
tanθ= b/a

Question 25

finding the Nth roots

Answer 25

nth root of r • [cos {(θ+360•n)/n} + i sin { } ]

K= 0,1,2,….,.n-1

Question 26

Distance btwn two points

Answer 26

_____________________

d= √ (x1-x2)^2 + (y1-y2)^2

Question 27

Arithmetic:
Nth term: An=
Sum of n terms=

Answer 27

An= a1 + (n-1)d
Sn= n/2 (a1+an)

Question 28

Geometric:
An=
Sn=
S∞=

Answer 28

An= a1•r^(n-1)
Sn= {a1(1-r^n)} / 1-r
S∞= a1/1-r

Question 29

Cofunctions

Answer 29

sinθ=cos(90-θ)
tan “ cot
cos “ sec

Question 30

Special Angles
30
45
60

Answer 30

pi/6
pi/4
pi/3