Linear Programming Day 2.
1. Dene the variables. What are you being askedfar?
2. Write the inequalities. Winn are the constraints on the variables?
3. Write the objective function. What are you trying to maximize?
4. Graph the system of inequalities. I: i
AlgebraTrig
Name_
Chapter2TestReview
Date_
Write the letter of the correct answer for each of the following problems:
1. Which syste m is incon si st ent?
A.
y = 0.5 x
x 2y = 1
B.
2x y = 8
4x + y = 5
C.
2. Which syste m ofequ ation s is shown by the graph
Algebra and Trigonometry
Trigonometric Identities
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An Identity represents two expressions that are equal for all values of the input.
Example:
(2 x + 1)3x = 6 x 2 + 3x
Trig Identities:
Reciprocals
1
sin =
csc
csc =
1
sin
cos =
1
sec
sec =
Algebra Trig
Working with Trig Identities
1. Find the indicated ratios.
tan = 1 ; Find cot
a.
4
b.
cos = 2 ; Find sin
3
c.
tan = 2 ; Find cos
5
d.
sin = 2 ; Find tan
7
Simplify each expression
sec
a.
csc
b.
csc 2 1
c.
sin cot + cos
d.
cos + sin tan
Algebra Trig
Verifying Trig Identities
Difference of Squares expressions
sin 2 x 1 = cos2 x
sec 2 x tan 2 x = 1
cot 2 x (cos 2 x 1) = cos 2 x
cos x(cos x sec 2 x + sec x ) = sec 2 x
Adding Fractional Expressions
sec 2 x
tan x
= cot x
tan x
sin 2 x
+ cos
Algebra & Trigonometry
7.5 Solving Trig Equations
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Date _
1
Trig equations are of the form cos x = 2 ; solve for x. There are several solutions.
Principal values lie between 0 and 2, and General values include all the angles between and .
1
cos x =
Algebra and Trigonometry
Chapter 7 Review
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1. Use the given information to determine the exact trig value requested:
2
5
cos = , sec
a.
b.
cot =
, tan
3
2
c.
1
sin = , cos
5
d.
tan =
e.
1
cos = , tan
8
f.
1
sin = , tan
3
b.
cos x cot x
Algebra and Trig
Trig Equations  Factoring
Solve the equations for the interval 0 x < 360
1.
sin 2 x + sin x = 0
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Date _
2.
3 tan x 3 tan 2 x = 0
3.
(2 cos x 1)(cos x + 1) = 0
4.
(csc x + 2)(csc x 2 ) = 0
5.
sec 2 x 3 sec x + 2 = 0
6.
sec 2 x + tan
Algebra and Trigonometry
6.3 Trigonometric Graphing
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Periodic Functions.
Periodic functions are those whose output values are repeated for regular intervals of the domain.
Can we identify the periodic functions from the group above?
a.
b.
c.
Algebra and Trigonometry
Writing Trig Equations
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Date _
Write two equations for the following.
1.
3
2
2.
1

Try writing two equations for the following:
b.
Write equations for the graphs shown.
2
4
2
3
2
3
1
1
2
2
A lgebra&Trig
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SineandC osineGraphing
S KILL #1
Date_
A is the amplitude; k changes the period: new period =
Graphtwoperiodsofthefollowing:
1.
2.
3.
4.
5.
6.
S KILL #2

Writinge quationsforthefollowing:
Example:GivenA=3andperiod=,writesineandc osin
Biorhythms and the Sine Curve Lab
16 points Due: _
TheTheoryofBiorhythmsstatesthatthereare3"cycles"toyourlife,whichstartedontheday
youwereborn:
The Physical Cycle:23dayslong
The Emotional Cycle:28dayslong
The Intellectual Cycle:33dayslong
Part 2: Biorhyt
Algebra & Trig
GRAPHING THE OTHER TRIG FUNCTIONS
Name _
cos
0
sin = y; cos = x;
y sin
tan = =
x cos
sin
0
1
4
2
3
4
2
2
2
2
1
0
5
4
3
2
7
4
2
2
2
0
2
2



2
2
1
2
2
1

0
2
2
0
2
2
1
Graph, label and indicate the asymptotes where necessary: f ( ) =
A lgebra Trig
_
Chapter 6 Trig Graphs Review
Name
Find the amplitude and period for the graphs below:
Amplitude =
; Period =
Write the new equations for the following:
1. , shifted up by 5 units
2. , shifted down by 3 units
3. , shifted left by
4. , shift
Algebra & Trigonometry
RM: A210
Mr. Sheldon Blackman
Classroom Expectations
1. Students are expected to be in class on time. Any entry after the bell is considered late.
2. There will be no eating, drinking, chewing gum, game playing or music in the class
Algebra & Trigonometry
2.1 Systems of Equations
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Graphical Solutions
The equation 4 x + 2 y = 32 describes the relation between two variables x and y. Identify points that are
solutions to this equation.
y
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
Algebra & Trigonometry
Solving Systems
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Date _
AMC Homes, Inc. is planning to build three and fourbedroom homes in a development called Heaven.
Consumer demand indicates a need for three times as many fourbedroom homes as for threebedroom
homes.
2.2 Solving Systems of 3 Variable Equations
* Equations of the form 2x 3y + 6z = 12 represent planes in space rather than lines in 2 dimensions. *
There will be an xintercept, a yintercept and a zintercept.
Algebra & Trigonometry
Solving Systems with Matrices
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Consider the following problem:
One weekend, the Goxfield Theater reported the following ticket sales for three movies, as shown in the table. If
the ticket prices were $6 for adults and $