Example 7: Using a Calculator to Solve Trigonometric Equations Solve the equation, correct to four decimal places, for 0
Example 7: Using a Calculator to Solve Trigonometric Equations Solve the equation, correct to four decimal places, for 0
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Topic Video
Question
Transcribed Image Text:PowerPoint
File
Edit
View
Insert
Format
Arrange
Tools
Slide Show
Window
Help
Wed Apr 28 6:22 PM
AutoSave
Chapter 5.5
OFF
lome
Insert
Draw
Design
Transitions
Animations
Slide Show
Review
View
Tell me
A Share
Comments
O Layout ♥
Arial (Body)
A A A
26
EE V
Shapes v
Reset
AV
A
Quick
Styles
Design
Ideas
Paste
New
U
ab-
v Aa v
Convert to
Picture
A Тext Boх
Arrange
Sensitivity
Slide
Section v
SmartArt
4 cos? x- 3 =0
The solutions in the interval [0,27)
for this equation are:
4 cos' x = 3
3
cos x
4
* 5x 77
6' 6
117
and
6
6
3
coS X =+.
V3
Example 7: Using a Calculator to
Solve Trigonometric Equations
O Pearson
Copyright o 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
Example 4: Using Factoring to
Separate Different Functions
Solve the equation: sin x tan x = sin x, 0s x < 2n.
Solution:
sin x tan x = sin x
tan x -1=0
on
sinx tanx - sin x = 0
sin x(tanx - 1) =0
sin x =0
X=0 X= T
tanx = 1
Solve the equation, correct to four decimal places, for
0<x< 2n.
57
4
4
The solutions for this equation in the interval (0,27)are:
5л
0,
T, and
4
O Pearon
Copyright 0 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
Example 5: Using an Identity to Solve
a Trigonometric Equation
Solution:
sin x is negative in quadrants III and IV
on
Solve the equation: cos 2x+ sin x = 0, 0sx< 2x.
Solution:cos 2x + sin x =0
1-2 sin' x + sin x =0
2 sin? x – sin x -1=0
(2sinx + 1)(sin x – 1) = 0
2sin x+1=0
2 sin x =-1
In quadrant II| X = T +0.2336
X × 3.3752
The solutions in the interval
sin x = -0.2315
[0,27) are
117
and
6
sin x-1=0
2' 6
sinx = 1
1
sinx =-
x = sin (-0.2315)
2
11
6
O Pearson
Copyright o 2018, 2014, 2010 Pearson Education, Inc. All Rights Reserved
Si- 12
In quadrant IV x × 2n – 1.2592
X = 6.0496
Example 6: Solving Trigonometric
Equations with a Calculator
X × 0.2336
Solve the equation, correct to four decimal places, for
Osx< 2n.
Solution:
tan x is positive in quadrants I and IlI
In quadrant I x =1.2592
tan x = 3.1044
n
x = tan (3.1044)
In quadrant III X =T+1.2592
* 4.4008
X= 1.2592
The solutions for this equation are 3.3752 and 6.0496.
The solutions for this equation are 1.2592 and 4.4008.
OPearn
Copyright o 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
P Pearson
Copyright © 2018, 2014, 2010 Pearson Education, Inc. All Rights Reserved
Slide - 14
Example 7: Using a Calculator to
Solve Trigonometric Equations
Solve the equation, correct to four decimal places, for
Osx<27.
Solution:
sin x is negative in quadrants Il and IV
Erample 6: Solving Trigonometric
with a
In quadrant III X=T+0.2336
X = 3.3752
Solve the eqton, comet r decimal places.
sin x = -0.2315
Click to add notes
an postive in quadratand
In quadrant -1.2592
x = sin '(-0.2315)
In quadrant IV x = 2 - 1.2592
X= 6.0496
X-lan 31044)
in t 12
12502
4.4008
X= 0.2336
The solutions for s equation are 125 and 4.400.
The solutions for this equation are 3.3752 and 6.0496.
O Pearson
Copyright o 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
Si- 14
12
Slide
APR
28
étv
A w
280
280
![PowerPoint
File
Edit
View
Insert
Format
Arrange
Tools
Slide Show
Window
Help
Wed Apr 28 6:22 PM
AutoSave
Chapter 5.5
OFF
lome
Insert
Draw
Design
Transitions
Animations
Slide Show
Review
View
Tell me
A Share
Comments
O Layout v
Arial (Body)
26
A A As
E v E= v
Shapes v
Reset
Quick
Styles
AV
A
Sensitivity
Design
Ideas
Paste
New
U
ab x
v Aa v
Convert to
Picture
[A] Text Box
Arrange
Slide
Section v
SmartArt
4 cos? x- 3 =0
The solutions in the interval [0,27)
for this equation are:
4 cos' x = 3
3
cos x
4
* 5x 77
6' 6
117
and
6
6
3
coS X =+.
V3
Example 6: Solving Trigonometric
Equations with a Calculator
O Pearson
Copyright o 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
Example 4: Using Factoring to
Separate Different Functions
Solve the equation: sin x tan x = sin x, 0s x < 2n.
Solution:
sin x tan x = sin x
tan x -1=0
on
sinx tanx - sin x = 0
sin x(tanx - 1) =0
sin x =0
X=0 X= T
tanx = 1
Solve the equation, correct to four decimal places, for
0<x< 2n.
57
4
4
The solutions for this equation in the interval (0,27)are:
5л
0,
T, and
4
O Pearon
Copyright 0 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
Solution:
Example 5: Using an Identity to Solve
a Trigonometric Equation
tan x is positive in quadrants I and III
on
Solve the equation: cos 2x+ sin x = 0, 0sx< 2x.
Solution:cos 2x + sin x =0
1-2sin' x+ sin x =0
2 sin? x – sin x -1=0
(2sinx + 1)(sin x – 1) = 0
2sin x+1=0
2 sin x =-1
tan x = 3.1044
In quadrant I x ×1.2592
The solutions in the interval
[0,27) are
117
and
6
sin x -1=0
2' 6
sinx = 1
1
sinx =-
x = tan (3.1044)
2
11x
X =
6
In quadrant Il| x = T +1.2592
z 4.4008
6
O Pearson
Copyright o 2018, 2014, 2010 Parson Education, Inc. All Rights Reserved
Si- 12
Example 6: Solving Trigonometric
Equations with a Calculator
X 1.2592
Solve the equation, correct to four decimal places, for
Osx<27.
Solution:
tan x is positive in quadrants I and II
In quadrant I x =1.2592
tan x = 3.1044
n
x = tan (3.1044)
In quadrant III X=T+1.2592
z 4.4008
X 1.2592
The solutions for this equation are 1.2592 and 4.4008.
The solutions for this equation are 1.2592 and 4.4008.
O Pearn
Copyright o 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved side- 13
P Pearson
Copyright © 2018, 2014, 2010 Pearson Education, Inc. All Rights Reserved
Slide - 13
Example 7: Using a Calculator to
Solve Trigonometric Equations
n
Solve the equation, correct to four decimal places, for
Osx<27.
Solution:
sin x is negative in quadrants IIl and IV
In quadrant III X=T+0.2336
X = 3.3752
sin x =-0,2315
Click to add notes
x = sin (-0.2315)
In quadrant IV X = 27 - 1.2592
X= 6.0496
X = 0.2336
The solutions for this equation are 3.3752 and 6.0496.
O Pearson
Copyright o 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
Side- 4
12
Slide
APR
28
étv A w
280
280
>](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67261072-26f7-4028-b56d-452c8cdeda03%2F2112007e-8b0d-42df-ba61-dddb3d34902c%2Fw9xfojb_processed.png&w=3840&q=75)
Transcribed Image Text:PowerPoint
File
Edit
View
Insert
Format
Arrange
Tools
Slide Show
Window
Help
Wed Apr 28 6:22 PM
AutoSave
Chapter 5.5
OFF
lome
Insert
Draw
Design
Transitions
Animations
Slide Show
Review
View
Tell me
A Share
Comments
O Layout v
Arial (Body)
26
A A As
E v E= v
Shapes v
Reset
Quick
Styles
AV
A
Sensitivity
Design
Ideas
Paste
New
U
ab x
v Aa v
Convert to
Picture
[A] Text Box
Arrange
Slide
Section v
SmartArt
4 cos? x- 3 =0
The solutions in the interval [0,27)
for this equation are:
4 cos' x = 3
3
cos x
4
* 5x 77
6' 6
117
and
6
6
3
coS X =+.
V3
Example 6: Solving Trigonometric
Equations with a Calculator
O Pearson
Copyright o 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
Example 4: Using Factoring to
Separate Different Functions
Solve the equation: sin x tan x = sin x, 0s x < 2n.
Solution:
sin x tan x = sin x
tan x -1=0
on
sinx tanx - sin x = 0
sin x(tanx - 1) =0
sin x =0
X=0 X= T
tanx = 1
Solve the equation, correct to four decimal places, for
0<x< 2n.
57
4
4
The solutions for this equation in the interval (0,27)are:
5л
0,
T, and
4
O Pearon
Copyright 0 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
Solution:
Example 5: Using an Identity to Solve
a Trigonometric Equation
tan x is positive in quadrants I and III
on
Solve the equation: cos 2x+ sin x = 0, 0sx< 2x.
Solution:cos 2x + sin x =0
1-2sin' x+ sin x =0
2 sin? x – sin x -1=0
(2sinx + 1)(sin x – 1) = 0
2sin x+1=0
2 sin x =-1
tan x = 3.1044
In quadrant I x ×1.2592
The solutions in the interval
[0,27) are
117
and
6
sin x -1=0
2' 6
sinx = 1
1
sinx =-
x = tan (3.1044)
2
11x
X =
6
In quadrant Il| x = T +1.2592
z 4.4008
6
O Pearson
Copyright o 2018, 2014, 2010 Parson Education, Inc. All Rights Reserved
Si- 12
Example 6: Solving Trigonometric
Equations with a Calculator
X 1.2592
Solve the equation, correct to four decimal places, for
Osx<27.
Solution:
tan x is positive in quadrants I and II
In quadrant I x =1.2592
tan x = 3.1044
n
x = tan (3.1044)
In quadrant III X=T+1.2592
z 4.4008
X 1.2592
The solutions for this equation are 1.2592 and 4.4008.
The solutions for this equation are 1.2592 and 4.4008.
O Pearn
Copyright o 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved side- 13
P Pearson
Copyright © 2018, 2014, 2010 Pearson Education, Inc. All Rights Reserved
Slide - 13
Example 7: Using a Calculator to
Solve Trigonometric Equations
n
Solve the equation, correct to four decimal places, for
Osx<27.
Solution:
sin x is negative in quadrants IIl and IV
In quadrant III X=T+0.2336
X = 3.3752
sin x =-0,2315
Click to add notes
x = sin (-0.2315)
In quadrant IV X = 27 - 1.2592
X= 6.0496
X = 0.2336
The solutions for this equation are 3.3752 and 6.0496.
O Pearson
Copyright o 2018, 2014, 2010 Pearson Education, Inc. AlI Rights Reserved
Side- 4
12
Slide
APR
28
étv A w
280
280
>
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
