Graphs of Sine and Cosine Functions
2.1 (Day 1)
Find:
sin 30 =
cos 30 =
(x, y)
(x, y) = (cos , sin )
sin =
cos =
tan =
csc =
sec =
cot =
Example 1
Find the exact value of each trig function.
a. sin 60
Basic Identities
3.1(Day 1)
Reciprocal Identities
1
1
sin x =
csc x =
csc x
sin x
cos x =
1
sec x =
sec x
tan x =
1
cos x
1
cot x =
cot x
1
tan x
In addition, tan x =
sin x
and cot x =
cos x
cos x
sin
Paired Data and Scatter Diagrams
3.1
Data from Example 1(pg. 128)
x = root depth
x
26.7
14
18
10.5
26.1
21.8
7
26
y
20.3
4.8
9
9
10.7
17.4
8.2
7.9
y = watermelon weight
x
13.9
19.3
17.5
13.1
16.5
28.4
Populations, Samples, and Data
1.1 (Day 1)
Statistics the study of how to collect, organize, analyze, and interpret numerical information.
Population all measurements or observations of interest.
Exam
An Introduction to Matrices
4.1
columns
2 3 5 6
C = 4 8 7 2 rows
1 0 5 9
Each value is called an Element
C3 x 4
Matrix Logic
Example 1
Jim, Mario, and Mike are married to Shana,
Kelly and Lisa. Use th
Distance and Midpoint Formula
7.1
Distance Formula
d
( x2 - x1 )
2
( y 2 - y1 )
2
Example 1
Find the distance between the points (4, 4) and (-6, -2).
Example 2
Find the value of a to make the distance
Solving Quadratic Equations by Graphing
6.1
Quadratic Function
f ( x) = ax 2 + bx + c
Write each in quadratic form.
Example 1
f ( x) = 3(x + 2)2
Example 2
Graph f ( x) = x 2 + 6x + 8
Example 3
An arro
Monomials
5.1
Express each in Scientific Notation
Example 1
236,000
Example 2
.001084
Monomial an algebraic expression that is a number, variable, or the product of a number and one or
more variables.
The Counting Principle
12.1
Solve problems by using the fundamental counting principle
Solve problems by using the strategy of solving a simpler problem
Dependent Events
Independent Events
Fundamental
Relations and Functions
2.1
4
A
B
2
D
-5
5
C
E
-2
F
-4
Relation a set of ordered pairs (Domain, Range).
Mapping shows how each number of the domain is paired with each member of the range.
Example 1
(
Real Exponents and Exponential Functions
10.1
Simplify expressions and solve equations involving real exponents
Exponential function
Exponential Function an equation of the form y = a b x where
a 0, b
Polynomial Functions
8.1
Polynomial in One Variable
a0 xn + a1xn 1 + a2 xn 2 + .an 1x + an
a0 , a1 , ., an - real numbers
Descending order
n must be a nonnegative integer
One variable.
Example 1
Deter
An Introduction to Trigonometry
13.1
Trig Identities
sin
opposite
cos
hypotenuse
csc
hypotenuse
adjacent
tan
adjacent
hypotenuse
sec
opposite
opposite
hypotenuse
cot
adjacent
adjacent
opposite
E
Solving Systems of Equations by Graphing
3.1
Systems of Equations a set of equations with the same variables.
Consistent System a system that has at least one solution.
Inconsistent System a system th
Graphing Rational Functions
9.1
Rational Function an equation in the form f ( x)
p ( x)
where p(x) and g(x) are polynomial functions.
g ( x)
Example 1
Example 2
x -1
Graph f ( x)
3
Graph f ( x)
x
Exam
Writing Equations
2.1
Addition
Subtraction
Multiplication
Example 1
A number b divided by three is six less than c.
Example 2
Fifteen more than z times 6 is 11 less than y times 2.
Example 3
Twenty su
Monomials and Factoring
8.1
Factored Form a monomial expressed as the product of prime numbers and variables (exponent
Example 1
Example 2
18x 2 y 3
24x3 y 5
Greatest Common Factor (GCF) the greatest
Solving Inequalities by Addition and Subtraction
5.1
, < =
, =
Example 1
c 12 > 65
Example 2
41 x + 17
Example 3
2a - 7 11
Example 4
5g - 16 < 9g
Example 5
3y + 7 > 8y - 23
Define a variable, write a
Multiplying Monomials
7.1
Monomial (1 Term) a number, a variable, or the product of a number and one or more variables
with non-negative integer exponents.
ex. -3, 7x, 5xy 2
Constant a monomial that i
Graphing Equations in Slope-Intercept Form
4.1
Slope-Intercept Form
y = mx + b
m = slope
b = y-intercept
Positive Slope
Negative Slope
0 slope
No Slope
Example 1
Write an equation in slope-intercept f
Graphing Linear Equations
3.1
Linear Equation an equation that forms a line when it is graphed.
Standard Form linear equations written in the form:
Ax + By = C
3 conditions to Standard Form
1. x and y
Graphing Quadratic Functions
9.1
Quadratic Functions - f ( x) = ax 2 + bx + c (also called standard form).
The graph of quadratic functions is called a parabola.
Axis of Symmetry a central line which
Graphing Systems of Equations
6.1
Systems of Equations a set of equations with the same variables.
Consistent System a system that has at least one solution.
Inconsistent System a system that does not
Simplifying Rational Expressions
11.3
Rational Expression an algebraic fraction whose numerator and denominator are polynomials.
*Since division by zero is undefined, the polynomial in the denominator
Square Root Functions
10.1
Square Root Function contains the square root of the variable.
Parent Function:
Type of Graph:
Domain:
Range:
f ( x) =
Curve
x
0
y
0
x
Example 1
Graph f ( x) = 2 x and state
The Law of Sines
5.1
Oblique Triangle a triangle without a right angle.
c
a
b
Law of Sines
sin
sin
sin
=
=
a
b
c
Example 1
Find the remaining parts of the triangle.
b. = 27, = 93, a = 12.6
a. = 51,