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
b. cos
4
c. tan
d. sec 0
6
Example 2
Find the coordina
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 x
Pythagorean Identities
2
2
sin x + cos x = 1
2
2
1 +
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
23.9
27
y
3.5
8.7
4.3
8.7
9.1
17.1
9.7
13.1
x
10.2
13.
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.
Example 1
If we want to know the average height of all who
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 these clues to find out
who is married to whom.
1. Mario
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 = 10 units given the points
(-7, 3) and (a, 11).
Examp
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 arrow is shot upward with an initial velocity of 64 ft / se
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.
ex. 12x, -8, 16a 2b3c
Constant (No Variables)
4, -9
Co
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 counting principle
Example 1
How many three-letter pat
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
(2, 4), (3, 0), (5, -2), (6, 0)
Function a special type
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 > 0, and b 1, is called an exponential function with 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
Determine if each expression is a polynomial in one variable
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
Example 1
Find the six trig functions for angle .
3 5
3
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 that does not have a solution.
Independent System a syste
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
Example 3
x( x - 3)
Example 4
2
x -9
Graph f ( x)
x+3
(x
Ex
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 subtracted from the product of 3 and x is 46.
Formula a r
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 number that is a factor of all original monomials.
Exam
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 an inequality, and solve.
Example 6
The difference of 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 is a real number.
ex. 8, -23
Determine whether each expr
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 form of the line with a slope of
2
and a y-intercept of
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 must be on the same side of equation
2. no fractions
3
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 makes the parabola symmetric.
Vertex the intersection o
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 have a solution.
Independent System a system that has
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 cannot be 0*
State the excluded value for each rationa
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 domain and range.
Example 2
Graph f ( x) =
1
x and
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, = 34, a = 9.4
Ambiguous Case (SSA or ASS)
= 43, b = 1
Introduction to Random Variables and Probability Distributions
5.1
Discrete random variable when the observations of a quantitative random number can take on only a finite number
of values or a countable number of values, we say it is a discrete random va
The Cartesian Coordinate System
P.1
Coordinate Plane
Ordered Pair
(x, y)
Example 1
Graph.
A (-3, 4)
B (0, -2)
C (2, -1)
D (4, 1)
E (-3, -2)
F (-5, 0)
Pythagorean Theorem
a 2 + b2 = c 2
Example 2
Solve
Example 3
Solve
6
b
c
4
3
3
Distance Formula
d = (x2 -
What is Probability?
4.1
Probability the likelihood that a certain event will occur.
P(A): P of A or Probability of A
0
P
1 or 0%
P
100%
Ways to Compute Probability
1. Intuition
Ex. ESPN reports that the Detroit Red Wings have a 70% chance of
Cup.
2. Rela