Lengths of Arcs and Areas of Sectors
Circumference of a circle = 2 p r
Area of a circle = p r2
THESE WORK WHEN YOURE DEALING WITH THE WHOLE CIRCLE!
Arc length of a sector: DEGREES: s =
RADIANS: s =
q
2p r
360
q
q 2p r q r
r= = =
2p
2p
2p 1
1
rq
*The form
Inverse Functions
Notes
EX. Use y = x2 to find the following values.
When x = 1, y = 1
When x = 2, y = 4
When x = 3, y = 9
Write this as a set of ordered pairs (x,y). cfw_(1, 1), (2, 4), (3, 9)
EX. Use x = y2 to find the following values.
When y = 1, x =
nth Root Functions Review
Def: Let n be an integer with n 2 . x is an nth root of k iff
EX 1:
xn = k.
_ is a 4th root of 81 because _
_ is a 3rd root of (-8) because _
n = odd means 1 root (always)
n = even means there may be 0, 1, or 2 roots
EX 2: (a)
(n
The Sine, Cosine, and Tangent Function Notes
f(x) = sin x,
f(x) = cos x,
f(x) = tan x,
(where x is a value of q on the unit circle)
4
y = sin x
2
Max = 1
-5
5
Min = 1
Period = 2 p
-2
x-intercepts = multiples of p
-4
y-intercept = (0, 0)
Amplitude = 1
Doma
Measures of Angles and Rotations
Review of Geometry:
uuu
r
uur
u
* BA is the rotation image of BC about point B
*360 degrees in a circle
*Counterclockwise (CCW) is the POSITIVE direction
*Clockwise (CW) is the NEGATIVE direction
* Q is the angle of rotati
The Factor Theorem Study Guide
Factor Theorem: For a polynomial f(x), the number c is a solution to f(x) = 0 if and only if (x c)
is a factor of f.
Ex. Look at graph of f(x) = x3 + x2 6x
Solutions to f(x) = 0 are the ZEROS of this graph
What are the zeros
Rational Power Functions
Rational Exponent Theorem: For any real number x > 0, and positive integers n and m,
m
1
1
m n
n
x = =( x ) = n x m
x
^- usually take the nth root first because it makes the #s smaller
m
n
This is read as the nth root of the mt
4-7 Scale-Change Images of Circular Functions
4-8 Translation Images of Circular Functions
Recall: TRANSFORMATIONS
Translation:
T(x, y) (x + h, y + k)
*substitute (x h) in the equation for x
*substitute (y k) in the equation for y
Scale Change:
S(x, y) (b
Properties of Logarithms Notes
We have seen rules and properties for exponential expressions. Because logarithms are inverses of
exponential functions, there are similar properties for logarithms.
EXPONENT PROPERTIES:
A:
LOGARITHM PROPERTIES:
Reflexive Pr
Step Functions
Pre Calc I (CP)
_
EX 1: You can fit 12 cans of soda in a box. Make a graph of cans (x) vs. number of
complete boxes (y).
Is this a function? _ Why / why not?
The greatest integer function is the function f such that for every real number x,