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
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. Us
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
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 = mu
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 (C
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
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 th
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
*substitu
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.
EXP
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 functi