Transcript Document

Overview of Second
Semester Math Analysis
Chapters 4, 5, and 6
Textbook:
Precalculus Functions and
Graphs:A Graphing
Approach
and
Precalculus with Limits:A
Graphing Approach
By Ron Larson, Robert P.
Hostetler, and Bruce H.
Edwards
Copyright 2001 by Houghton Mifflin Company.
Chapters
 Chapter
4
 Chapter
5
 Chapter
6
 Online
Notebook Organizer
Chapters
Radian and Degree Measure
 Chapter
4
Trigonometric Functions: The Unit
Circle
Right Triangle Trigonometry
 Chapter
5
Trigonometric Functions of Any Angle
Graphs of Sine and Cosine Functions
 Chapter
6
Graphs of Other Trigonometric
Functions
Inverse Trigonometric Functions
 Online
Notebook Organizer
Chapters
 Chapter
4
Using Fundamental Identities
Verifying Trigonometric Identities
 Chapter
5
Solving Trigonometric Equations
Sum and Difference Formulas
 Chapter
 Online
6
Multiple-Angle and Product-Sum
Formulas
Notebook Organizer
Chapters
 Chapter
4
Law of Sines
 Chapter
5
Law of Cosines
Areas of Right and Oblique Triangles
 Chapter
 Online
6
Notebook Organizer
Chapters
 Chapter
4
 Chapter
5
 Chapter
6
 Online
This online notebook organizer is a
set of templates that will help you
develop a section-by-section
summary of the key concepts of the
included chapters from the textbook.
Click on the link below to use this
tool:
http://college.hmco.com/mathematics
/larson/precalculus_functions_aga/3e
/students/sso.html
Notebook Organizer
Review Exercises
1. The height of a tree can be determined by measuring the
length of the shadow of the tree and the angle of elevation
of the sun from the tip of the shadow. Find the height of a
tree that casts a 20 foot shadow when the angle of elevation
is 600.
a. 17.32 feet
b. 34.64 feet
h=?
600
c. 30 feet
d. 28.28 feet
Review Exercises
1. The height of a tree can be determined by measuring the
length of the shadow of the tree and the angle of elevation
of the sun from the tip of the shadow. Find the height of a
tree that casts a 20 foot shadow when the angle of elevation
is 600.
a. 17.32 feet
b. 34.64 feet
h=?
600
c. 30 feet
d. 28.28 feet
Review Exercises
1. The height of a tree can be determined by measuring the
length of the shadow of the tree and the angle of elevation
of the sun from the tip of the shadow. Find the height of a
tree that casts a 20 foot shadow when the angle of elevation
is 600.
a. 17.32 feet 
b. 34.64 feet
h=?
600
c. 30 feet
d. 28.28 feet
Review Exercises
1. The height of a tree can be determined by measuring the
length of the shadow of the tree and the angle of elevation
of the sun from the tip of the shadow. Find the height of a
tree that casts a 20 foot shadow when the angle of elevation
is 600.
a. 17.32 feet
b. 34.64 feet 
h=?
600
c. 30 feet
d. 28.28 feet
Review Exercises
1. The height of a tree can be determined by measuring the
length of the shadow of the tree and the angle of elevation
of the sun from the tip of the shadow. Find the height of a
tree that casts a 20 foot shadow when the angle of elevation
is 600.
a. 17.32 feet
b. 34.64 feet
h=?
600
c. 30 feet 
d. 28.28 feet
Review Exercises
1. The height of a tree can be determined by measuring the
length of the shadow of the tree and the angle of elevation
of the sun from the tip of the shadow. Find the height of a
tree that casts a 20 foot shadow when the angle of elevation
is 600.
a. 17.32 feet
b. 34.64 feet
h=?
600
c. 30 feet
d. 28.28 feet 
Review Exercises
2. Standing on a dock 10 feet above the water line, you sight a
ship heading directly toward you. Let x be the angle of
depression to the ship and d the distance from the shore to
the ship. Write d as a function of x.
a. d = tan x / 10
b. d = 10 tan x
10 feet
x
d
Photo from www.freefoto.com
c. d = 10 cot x
d. d = cot x / 10
Review Exercises
2. Standing on a dock 10 feet above the water line, you sight a
ship heading directly toward you. Let x be the angle of
depression to the ship and d the distance from the shore to
the ship. Write d as a function of x.
a. d = tan x / 10
b. d = 10 tan x
10 feet
x
d
Photo from www.freefoto.com
c. d = 10 cot x
d. d = cot x / 10
Review Exercises
2. Standing on a dock 10 feet above the water line, you sight a
ship heading directly toward you. Let x be the angle of
depression to the ship and d the distance from the shore to
the ship. Write d as a function of x.
a. d = tan x / 10 
b. d = 10 tan x
10 feet
x
d
Photo from www.freefoto.com
c. d = 10 cot x
d. d = cot x / 10
Review Exercises
2. Standing on a dock 10 feet above the water line, you sight a
ship heading directly toward you. Let x be the angle of
depression to the ship and d the distance from the shore to
the ship. Write d as a function of x.
a. d = tan x / 10
b. d = 10 tan x 
10 feet
x
d
Photo from www.freefoto.com
c. d = 10 cot x
d. d = cot x / 10
Review Exercises
2. Standing on a dock 10 feet above the water line, you sight a
ship heading directly toward you. Let x be the angle of
depression to the ship and d the distance from the shore to
the ship. Write d as a function of x.
a. d = tan x / 10
b. d = 10 tan x
10 feet
x
d
Photo from www.freefoto.com
c. d = 10 cot x 
d. d = cot x / 10
Review Exercises
2. Standing on a dock 10 feet above the water line, you sight a
ship heading directly toward you. Let x be the angle of
depression to the ship and d the distance from the shore to
the ship. Write d as a function of x.
a. d = tan x / 10
b. d = 10 tan x
10 feet
x
d
Photo from www.freefoto.com
c. d = 10 cot x
d. d = cot x / 10 
Review Exercises
3. Convert the angle measure 3 / 8 to degrees.
a. 67.50
b. 1.180
c. 1350
Photo from www.freefoto.com
d. 750
Review Exercises
3. Convert the angle measure 3 / 8 to degrees.
a. 67.50
b. 1.180
c. 1350
Photo from www.freefoto.com
d. 750
Review Exercises
3. Convert the angle measure 3 / 8 to degrees.
a. 67.50 
b. 1.180
c. 1350
Photo from www.freefoto.com
d. 750
Review Exercises
3. Convert the angle measure 3 / 8 to degrees.
a. 67.50
b. 1.180 
c. 1350
Photo from www.freefoto.com
d. 750
Review Exercises
3. Convert the angle measure 3 / 8 to degrees.
a. 67.50
b. 1.180
c. 1350 
Photo from www.freefoto.com
d. 750
Review Exercises
3. Convert the angle measure 3 / 8 to degrees.
a. 67.50
b. 1.180
c. 1350
Photo from www.freefoto.com
d. 750 
Review Exercises
4. Find the point ( x, y ) on the unit circle that corresponds to
the real number t = 17 / 6.
a. ( 1, -1)
b. ( 0, -1)
c. ( -1, 0)
Clip Art from www.freemediagoo.com
d. ( -1, 1)
Review Exercises
4. Find the point ( x, y ) on the unit circle that corresponds to
the real number t = 17 / 6.
a. ( 1, -1)
b. ( 0, -1)
c. ( -1, 0)
Clip Art from www.freemediagoo.com
d. ( -1, 1)
Review Exercises
4. Find the point ( x, y ) on the unit circle that corresponds to
the real number t = 17 / 6.
a. ( 1, -1) 
b. ( 0, -1)
c. ( -1, 0)
Clip Art from www.freemediagoo.com
d. ( -1, 1)
Review Exercises
4. Find the point ( x, y ) on the unit circle that corresponds to
the real number t = 17 / 6.
a. ( 1, -1)
b. ( 0, -1) 
c. ( -1, 0)
Clip Art from www.freemediagoo.com
d. ( -1, 1)
Review Exercises
4. Find the point ( x, y ) on the unit circle that corresponds to
the real number t = 17 / 6.
a. ( 1, -1)
b. ( 0, -1)
c. ( -1, 0) 
Clip Art from www.freemediagoo.com
d. ( -1, 1)
Review Exercises
4. Find the point ( x, y ) on the unit circle that corresponds to
the real number t = 17 / 6.
a. ( 1, -1)
b. ( 0, -1)
c. ( -1, 0)
Clip Art from www.freemediagoo.com
d. ( -1, 1) 
Review Exercises
5. Determine the period and amplitude of the graph shown
below.
3
2
a. period: 6, amplitude: /2
1
-1
-2
-3
π
8
3π
8
5π
8
7π
8
b. period: /4, amplitude: 3
c. period: /2 , amplitude: 3
d. period: 3, amplitude: /2
Review Exercises
5. Determine the period and amplitude of the graph shown
below.
3
2
a. period: 6, amplitude: /2
1
-1
-2
-3
π
8
3π
8
5π
8
7π
8
b. period: /4, amplitude: 3
c. period: /2 , amplitude: 3
d. period: 3, amplitude: /2
Review Exercises
5. Determine the period and amplitude of the graph shown
below.
3
2
a. period: 6, amplitude: /2 
1
-1
-2
-3
π
8
3π
8
5π
8
7π
8
b. period: /4, amplitude: 3
c. period: /2 , amplitude: 3
d. period: 3, amplitude: /2
Review Exercises
5. Determine the period and amplitude of the graph shown
below.
3
2
a. period: 6, amplitude: /2
1
-1
-2
-3
π
8
3π
8
5π
8
7π
8
b. period: /4, amplitude: 3 
c. period: /2 , amplitude: 3
d. period: 3, amplitude: /2
Review Exercises
5. Determine the period and amplitude of the graph shown
below.
3
2
a. period: 6, amplitude: /2
1
-1
-2
-3
π
8
3π
8
5π
8
7π
8
b. period: /4, amplitude: 3
c. period: /2 , amplitude: 3 
d. period: 3, amplitude: /2
Review Exercises
5. Determine the period and amplitude of the graph shown
below.
3
2
a. period: 6, amplitude: /2
1
-1
-2
-3
π
8
3π
8
5π
8
7π
8
b. period: /4, amplitude: 3
c. period: /2 , amplitude: 3
d. period: 3, amplitude: /2
Review Exercises
6. A surveyor wishes to find the distance across the river. The
bearings from 2 points 70 feet apart on the same bank of the
river to a tree on the opposite bank are N and N 340 W. Find
the width of the river.
N
a. 93.4 feet
b. 100.9 feet

?

560

Photo from www.freemediagoo.com
c. 103.8 feet
d. 111.4 feet
Review Exercises
6. A surveyor wishes to find the distance across the river. The
bearings from 2 points 70 feet apart on the same bank of the
river to a tree on the opposite bank are N and N 340 W. Find
the width of the river.
N
N
b. 100.9 feet

?

a. 93.4 feet
560

Photo from www.freemediagoo.com
c. 103.8 feet
d. 111.4 feet
Review Exercises
6. A surveyor wishes to find the distance across the river. The
bearings from 2 points 70 feet apart on the same bank of the
river to a tree on the opposite bank are N and N 340 W. Find
the width of the river.
N
N
b. 100.9 feet

?

a. 93.4 feet 
560

Photo from www.freemediagoo.com
c. 103.8 feet
d. 111.4 feet
Review Exercises
6. A surveyor wishes to find the distance across the river. The
bearings from 2 points 70 feet apart on the same bank of the
river to a tree on the opposite bank are N and N 340 W. Find
the width of the river.
N
N
b. 100.9 feet 

?

a. 93.4 feet
560

Photo from www.freemediagoo.com
c. 103.8 feet
d. 111.4 feet
Review Exercises
6. A surveyor wishes to find the distance across the river. The
bearings from 2 points 70 feet apart on the same bank of the
river to a tree on the opposite bank are N and N 340 W. Find
the width of the river.
N
N
b. 100.9 feet

?

a. 93.4 feet
560

Photo from www.freemediagoo.com
c. 103.8 feet 
d. 111.4 feet
Review Exercises
6. A surveyor wishes to find the distance across the river. The
bearings from 2 points 70 feet apart on the same bank of the
river to a tree on the opposite bank are N and N 340 W. Find
the width of the river.
N
N
b. 100.9 feet

?

a. 93.4 feet
560

Photo from www.freemediagoo.com
c. 103.8 feet
d. 111.4 feet
Review Exercises
7.A sea-to-air guided missile shot from a submarine breaks the
water surface at an angle of elevation of 20.40 traveling at
520 feet per second. If the missile continues at a constant
angle and at the same speed, how far above sea level will it
be after 20 seconds?
a. 4500.3 feet
b. 1005.2 feet
c. 500.75 feet
Photo from http://gimp-savvy.com
d. 3625.1 feet
Review Exercises
7.A sea-to-air guided missile shot from a submarine breaks the
water surface at an angle of elevation of 20.40 traveling at
520 feet per second. If the missile continues at a constant
angle and at the same speed, how far above sea level will it
be after 20 seconds?
a. 4500.3 feet
b. 1005.2 feet
c. 500.75 feet
Photo from http://gimp-savvy.com
d. 3625.1 feet
Review Exercises
7.A sea-to-air guided missile shot from a submarine breaks the
water surface at an angle of elevation of 20.40 traveling at
520 feet per second. If the missile continues at a constant
angle and at the same speed, how far above sea level will it
be after 20 seconds?
N
a. 4500.3 feet 
b. 1005.2 feet
c. 500.75 feet
Photo from http://gimp-savvy.com
d. 3625.1 feet
Review Exercises
7.A sea-to-air guided missile shot from a submarine breaks the
water surface at an angle of elevation of 20.40 traveling at
520 feet per second. If the missile continues at a constant
angle and at the same speed, how far above sea level will it
be after 20 seconds?
N
a. 4500.3 feet
b. 1005.2 feet 
c. 500.75 feet
Photo from http://gimp-savvy.com
d. 3625.1 feet
Review Exercises
7.A sea-to-air guided missile shot from a submarine breaks the
water surface at an angle of elevation of 20.40 traveling at
520 feet per second. If the missile continues at a constant
angle and at the same speed, how far above sea level will it
be after 20 seconds?
N
a. 4500.3 feet
b. 1005.2 feet
c. 500.75 feet 
Photo from http://gimp-savvy.com
d. 3625.1 feet
Review Exercises
7.A sea-to-air guided missile shot from a submarine breaks the
water surface at an angle of elevation of 20.40 traveling at
520 feet per second. If the missile continues at a constant
angle and at the same speed, how far above sea level will it
be after 20 seconds?
N
a. 4500.3 feet
b. 1005.2 feet
c. 500.75 feet
Photo from http://gimp-savvy.com
d. 3625.1 feet 
Review Exercises
8. Given cot x is undefined, and cos x > 0, find csc x.
a. 0
b. 1
c. -1
d. undefined
Review Exercises
8. Given cot x is undefined, and cos x > 0, find csc x.
a. 0
b. 1
c. -1
d. undefined
Review Exercises
8. Given cot x is undefined, and cos x > 0, find csc x.
N
a. 0 
b. 1
c. -1
d. undefined
Review Exercises
8. Given cot x is undefined, and cos x > 0, find csc x.
N
a. 0
b. 1 
c. -1
d. undefined
Review Exercises
8. Given cot x is undefined, and cos x > 0, find csc x.
N
a. 0
b. 1
c. -1 
d. undefined
Review Exercises
8. Given cot x is undefined, and cos x > 0, find csc x.
N
a. 0
b. 1
c. -1
d. undefined 
Review Exercises
9. Find all solutions in the interval [0, 2 ) :
csc2 x - (cos4 x + cos2 x sin2 x + sin4 x) = 0.
a. /2, 3/2
b. 0, 
c. /4, 3/4, 5/4, 7/4
Photo from www.freefoto.com
d. /2
Review Exercises
9. Find all solutions in the interval [0, 2 ) :
csc2 x - (cos4 x + cos2 x sin2 x + sin4 x) = 0.
a. /2, 3/2
b. 0, 
c. /4, 3/4, 5/4, 7/4
Photo from www.freefoto.com
d. /2
Review Exercises
9. Find all solutions in the interval [0, 2 ) :
csc2 x - (cos4 x + cos2 x sin2 x + sin4 x) = 0.
N
a. /2, 3/2 
b. 0, 
c. /4, 3/4, 5/4, 7/4
Photo from www.freefoto.com
d. /2
Review Exercises
9. Find all solutions in the interval [0, 2 ) :
csc2 x - (cos4 x + cos2 x sin2 x + sin4 x) = 0.
N
a. /2, 3/2
b. 0,  
c. /4, 3/4, 5/4, 7/4
Photo from www.freefoto.com
d. /2
Review Exercises
9. Find all solutions in the interval [0, 2 ) :
csc2 x - (cos4 x + cos2 x sin2 x + sin4 x) = 0.
N
a. /2, 3/2
b. 0, 
c. /4, 3/4, 5/4, 7/4 
Photo from www.freefoto.com
d. /2
Review Exercises
9. Find all solutions in the interval [0, 2 ) :
csc2 x - (cos4 x + cos2 x sin2 x + sin4 x) = 0.
N
a. /2, 3/2
b. 0, 
c. /4, 3/4, 5/4, 7/4
Photo from www.freefoto.com
d. /2 
Review Exercises
10. Find the height of a giant helium balloon used in a
Thanksgiving Day parade given that two guy wires are
attached as shown in the figure below.
a. 115.9 feet
b. 200.3 feet
300
490
100 feet
Photo from www.readio.com
c. 175.6 feet
d. 100 feet
Review Exercises
10. Find the height of a giant helium balloon used in a
Thanksgiving Day parade given that two guy wires are
attached as shown in the figure below.
a. 115.9 feet
b. 200.3 feet
300
490
100 feet
Photo from www.readio.com
c. 175.6 feet
d. 100 feet
Review Exercises
10. Find the height of a giant helium balloon used in a
Thanksgiving Day parade given that two guy wires are
attached as shown in the figure below.
N
a. 115.9 feet 
b. 200.3 feet
300
490
100 feet
Photo from www.readio.com
c. 175.6 feet
d. 100 feet
Review Exercises
10. Find the height of a giant helium balloon used in a
Thanksgiving Day parade given that two guy wires are
attached as shown in the figure below.
N
a. 115.9 feet
b. 200.3 feet 
300
490
100 feet
Photo from www.readio.com
c. 175.6 feet
d. 100 feet
Review Exercises
10. Find the height of a giant helium balloon used in a
Thanksgiving Day parade given that two guy wires are
attached as shown in the figure below.
N
a. 115.9 feet
b. 200.3 feet
300
490
100 feet
Photo from www.readio.com
c. 175.6 feet 
d. 100 feet
Review Exercises
10. Find the height of a giant helium balloon used in a
Thanksgiving Day parade given that two guy wires are
attached as shown in the figure below.
N
a. 115.9 feet
b. 200.3 feet
300
490
100 feet
Photo from www.readio.com
c. 175.6 feet
d. 100 feet 
Edit 241 Final Project
EmergingTechnologies for
References:
1.
Precalculus Functions and Graphs: A
Graphing Approach by Ron Larson,
Robert P. Hostetler, and Bruce H.
Edwards
2.
Test Item File by Anne Larson Quinn
3.
Student Success Organizer (online) from
Houghton Mifflin Company
Sources of photos and clip arts cited on the
slides.
Teachers
Rebecca T. Macasaet