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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)
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°.
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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
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 >
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 >
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