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High School Math Calculus Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

x by solving the equation for 0 ≤ x < 2 π .

x by solving the equation for 0 ≤ x < 2 π .

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 7.5, Problem 31E

To determine

To find: x by solving the equation for $0≤x<2π$ .

Expert Solution & Answer

Answer to Problem 31E

$7π6 and 11π6$

Explanation of Solution

Given information:

$4sin2x+1=−4sinx$

Calculation:

The value of x for the given equation can be evaluated as follows:

$4sin2x+1=−4sinx [Add 4sinx on each side]$

$4sin2x+4sinx+1=0$

$(2sinx+1)2=0 [Using (a+b)2=a2+b2+2ab]$

$2sinx+1=0 [Taking square root on each side]$

$2sinx=−1 [Subtract 1 from each side]$

$sinx=−12 [Divide each side by 2]$

$x=7π6 or 11π6$

Thus the values of x are $7π6 and 11π6$ .

Chapter 7.5, Problem 30E

Chapter 7.5, Problem 32E

Chapter 7 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 7.1 - Prob. 1CFU Ch. 7.1 - Prob. 2CFU Ch. 7.1 - Prob. 3CFU Ch. 7.1 - Prob. 4CFU Ch. 7.1 - Prob. 5CFU Ch. 7.1 - Prob. 6CFU Ch. 7.1 - Prob. 7CFU Ch. 7.1 - Prob. 8CFU Ch. 7.1 - Prob. 9CFU Ch. 7.1 - Prob. 10CFU

Ch. 7.1 - Prob. 11CFU Ch. 7.1 - Prob. 12CFU Ch. 7.1 - Prob. 13CFU Ch. 7.1 - Prob. 14CFU Ch. 7.1 - Prob. 15CFU Ch. 7.1 - Prob. 16CFU Ch. 7.1 - Prob. 17CFU Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - Prob. 61E Ch. 7.1 - Prob. 62E Ch. 7.1 - Prob. 63E Ch. 7.1 - Prob. 64E Ch. 7.1 - Prob. 65E Ch. 7.1 - Prob. 66E Ch. 7.1 - Prob. 67E Ch. 7.1 - Prob. 68E Ch. 7.1 - Prob. 69E Ch. 7.2 - Prob. 1GCE Ch. 7.2 - Prob. 2GCE Ch. 7.2 - Prob. 3GCE Ch. 7.2 - Prob. 4GCE Ch. 7.2 - Prob. 5GCE Ch. 7.2 - Prob. 1CFU Ch. 7.2 - Prob. 2CFU Ch. 7.2 - Prob. 3CFU Ch. 7.2 - Prob. 4CFU Ch. 7.2 - Prob. 5CFU Ch. 7.2 - Prob. 6CFU Ch. 7.2 - Prob. 7CFU Ch. 7.2 - Prob. 8CFU Ch. 7.2 - Prob. 9CFU Ch. 7.2 - Prob. 10CFU Ch. 7.2 - Prob. 11CFU Ch. 7.2 - Prob. 12CFU Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - Prob. 18E Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - Prob. 23E Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - Prob. 26E Ch. 7.2 - Prob. 27E Ch. 7.2 - Prob. 28E Ch. 7.2 - Prob. 29E Ch. 7.2 - Prob. 30E Ch. 7.2 - Prob. 31E Ch. 7.2 - Prob. 32E Ch. 7.2 - Prob. 33E Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Prob. 36E Ch. 7.2 - Prob. 37E Ch. 7.2 - Prob. 38E Ch. 7.2 - Prob. 39E Ch. 7.2 - Prob. 40E Ch. 7.2 - Prob. 41E Ch. 7.2 - Prob. 42E Ch. 7.2 - Prob. 43E Ch. 7.2 - Prob. 44E Ch. 7.2 - Prob. 45E Ch. 7.2 - Prob. 46E Ch. 7.2 - Prob. 47E Ch. 7.2 - Prob. 48E Ch. 7.2 - Prob. 49E Ch. 7.2 - Prob. 50E Ch. 7.2 - Prob. 51E Ch. 7.2 - Prob. 52E Ch. 7.2 - Prob. 53E Ch. 7.3 - Prob. 1CFU Ch. 7.3 - Prob. 2CFU Ch. 7.3 - Prob. 3CFU Ch. 7.3 - Prob. 4CFU Ch. 7.3 - Prob. 5CFU Ch. 7.3 - Prob. 6CFU Ch. 7.3 - Prob. 7CFU Ch. 7.3 - Prob. 8CFU Ch. 7.3 - Prob. 9CFU Ch. 7.3 - Prob. 10CFU Ch. 7.3 - Prob. 11CFU Ch. 7.3 - Prob. 12CFU Ch. 7.3 - Prob. 13CFU Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - Prob. 25E Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Prob. 30E Ch. 7.3 - Prob. 31E Ch. 7.3 - Prob. 32E Ch. 7.3 - Prob. 33E Ch. 7.3 - Prob. 34E Ch. 7.3 - Prob. 35E Ch. 7.3 - Prob. 36E Ch. 7.3 - Prob. 37E Ch. 7.3 - Prob. 38E Ch. 7.3 - Prob. 39E Ch. 7.3 - Prob. 40E Ch. 7.3 - Prob. 41E Ch. 7.3 - Prob. 42E Ch. 7.3 - Prob. 43E Ch. 7.3 - Prob. 44E Ch. 7.3 - Prob. 45E Ch. 7.3 - Prob. 46E Ch. 7.3 - Prob. 47E Ch. 7.3 - Prob. 48E Ch. 7.3 - Prob. 49E Ch. 7.3 - Prob. 50E Ch. 7.3 - Prob. 51E Ch. 7.3 - Prob. 52E Ch. 7.3 - Prob. 53E Ch. 7.3 - Prob. 54E Ch. 7.3 - Prob. 55E Ch. 7.3 - Prob. 56E Ch. 7.3 - Prob. 57E Ch. 7.3 - Prob. 58E Ch. 7.3 - Prob. 59E Ch. 7.3 - Prob. 60E Ch. 7.3 - Prob. 61E Ch. 7.3 - Prob. 62E Ch. 7.3 - Prob. 63E Ch. 7.3 - Prob. 64E Ch. 7.3 - Prob. 1MCQ Ch. 7.3 - Prob. 2MCQ Ch. 7.3 - Prob. 3MCQ Ch. 7.3 - Prob. 4MCQ Ch. 7.3 - Prob. 5MCQ Ch. 7.3 - Prob. 6MCQ Ch. 7.3 - Prob. 7MCQ Ch. 7.3 - Prob. 8MCQ Ch. 7.3 - Prob. 9MCQ Ch. 7.3 - Prob. 10MCQ Ch. 7.3B - Prob. 1GCE Ch. 7.3B - Prob. 2GCE Ch. 7.3B - Prob. 3GCE Ch. 7.3B - Prob. 4GCE Ch. 7.3B - Prob. 5GCE Ch. 7.3B - Prob. 6GCE Ch. 7.3B - Prob. 7GCE Ch. 7.3B - Prob. 8GCE Ch. 7.4 - Prob. 1CFU Ch. 7.4 - Prob. 2CFU Ch. 7.4 - Prob. 3CFU Ch. 7.4 - Prob. 4CFU Ch. 7.4 - Prob. 5CFU Ch. 7.4 - Prob. 6CFU Ch. 7.4 - Prob. 7CFU Ch. 7.4 - Prob. 8CFU Ch. 7.4 - Prob. 9CFU Ch. 7.4 - Prob. 10CFU Ch. 7.4 - Prob. 11CFU Ch. 7.4 - Prob. 12CFU Ch. 7.4 - Prob. 13CFU Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Prob. 22E Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Prob. 28E Ch. 7.4 - Prob. 29E Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Prob. 33E Ch. 7.4 - Prob. 34E Ch. 7.4 - Prob. 35E Ch. 7.4 - Prob. 36E Ch. 7.4 - Prob. 37E Ch. 7.4 - Prob. 38E Ch. 7.4 - Prob. 39E Ch. 7.4 - Prob. 40E Ch. 7.4 - Prob. 41E Ch. 7.4 - Prob. 42E Ch. 7.4 - Prob. 43E Ch. 7.4 - Prob. 44E Ch. 7.4 - Prob. 45E Ch. 7.4 - Prob. 46E Ch. 7.4 - Prob. 47E Ch. 7.4 - Prob. 48E Ch. 7.5 - Prob. 1GCE Ch. 7.5 - Prob. 2GCE Ch. 7.5 - Prob. 3GCE Ch. 7.5 - Prob. 4GCE Ch. 7.5 - Prob. 5GCE Ch. 7.5 - Prob. 1CFU Ch. 7.5 - Prob. 2CFU Ch. 7.5 - Prob. 3CFU Ch. 7.5 - Prob. 4CFU Ch. 7.5 - Prob. 5CFU Ch. 7.5 - Prob. 6CFU Ch. 7.5 - Prob. 7CFU Ch. 7.5 - Prob. 8CFU Ch. 7.5 - Prob. 9CFU Ch. 7.5 - Prob. 10CFU Ch. 7.5 - Prob. 11CFU Ch. 7.5 - Prob. 12E Ch. 7.5 - Prob. 13E Ch. 7.5 - Prob. 14E Ch. 7.5 - Prob. 15E Ch. 7.5 - Prob. 16E Ch. 7.5 - Prob. 17E Ch. 7.5 - Prob. 18E Ch. 7.5 - Prob. 19E Ch. 7.5 - Prob. 20E Ch. 7.5 - Prob. 21E Ch. 7.5 - Prob. 22E Ch. 7.5 - Prob. 23E Ch. 7.5 - Prob. 24E Ch. 7.5 - Prob. 25E Ch. 7.5 - Prob. 26E Ch. 7.5 - Prob. 27E Ch. 7.5 - Prob. 28E Ch. 7.5 - Prob. 29E Ch. 7.5 - Prob. 30E Ch. 7.5 - Prob. 31E Ch. 7.5 - Prob. 32E Ch. 7.5 - Prob. 33E Ch. 7.5 - Prob. 34E Ch. 7.5 - Prob. 35E Ch. 7.5 - Prob. 36E Ch. 7.5 - Prob. 37E Ch. 7.5 - Prob. 38E Ch. 7.5 - Prob. 39E Ch. 7.5 - Prob. 40E Ch. 7.5 - Prob. 41E Ch. 7.5 - Prob. 42E Ch. 7.5 - Prob. 43E Ch. 7.5 - Prob. 44E Ch. 7.5 - Prob. 45E Ch. 7.5 - Prob. 46E Ch. 7.5 - Prob. 47E Ch. 7.5 - Prob. 48E Ch. 7.5 - Prob. 49E Ch. 7.5 - Prob. 50E Ch. 7.5 - Prob. 51E Ch. 7.5 - Prob. 52E Ch. 7.5 - Prob. 53E Ch. 7.5 - Prob. 54E Ch. 7.5 - Prob. 55E Ch. 7.5 - Prob. 56E Ch. 7.5 - Prob. 57E Ch. 7.5 - Prob. 58E Ch. 7.5 - Prob. 59E Ch. 7.5 - Prob. 60E Ch. 7.5 - Prob. 61E Ch. 7.5 - Prob. 62E Ch. 7.5 - Prob. 63E Ch. 7.5 - Prob. 64E Ch. 7.5 - Prob. 65E Ch. 7.5 - Prob. 66E Ch. 7.5 - Prob. 67E Ch. 7.5 - Prob. 68E Ch. 7.5 - Prob. 69E Ch. 7.5 - Prob. 70E Ch. 7.5 - Prob. 71E Ch. 7.5 - Prob. 72E Ch. 7.6 - Prob. 1CFU Ch. 7.6 - Prob. 2CFU Ch. 7.6 - Prob. 3CFU Ch. 7.6 - Prob. 4CFU Ch. 7.6 - Prob. 5CFU Ch. 7.6 - Prob. 6CFU Ch. 7.6 - Prob. 7CFU Ch. 7.6 - Prob. 8CFU Ch. 7.6 - Prob. 9CFU Ch. 7.6 - Prob. 10CFU Ch. 7.6 - Prob. 11CFU Ch. 7.6 - Prob. 12CFU Ch. 7.6 - Prob. 13CFU Ch. 7.6 - Prob. 14CFU Ch. 7.6 - Prob. 15CFU Ch. 7.6 - Prob. 16E Ch. 7.6 - Prob. 17E Ch. 7.6 - Prob. 18E Ch. 7.6 - Prob. 19E Ch. 7.6 - Prob. 20E Ch. 7.6 - Prob. 21E Ch. 7.6 - Prob. 22E Ch. 7.6 - Prob. 23E Ch. 7.6 - Prob. 24E Ch. 7.6 - Prob. 25E Ch. 7.6 - Prob. 26E Ch. 7.6 - Prob. 27E Ch. 7.6 - Prob. 28E Ch. 7.6 - Prob. 29E Ch. 7.6 - Prob. 30E Ch. 7.6 - Prob. 31E Ch. 7.6 - Prob. 32E Ch. 7.6 - Prob. 33E Ch. 7.6 - Prob. 34E Ch. 7.6 - Prob. 35E Ch. 7.6 - Prob. 36E Ch. 7.6 - Prob. 37E Ch. 7.6 - Prob. 38E Ch. 7.6 - Prob. 39E Ch. 7.6 - Prob. 40E Ch. 7.6 - Prob. 41E Ch. 7.6 - Prob. 42E Ch. 7.6 - Prob. 43E Ch. 7.6 - Prob. 44E Ch. 7.6 - Prob. 45E Ch. 7.6 - Prob. 46E Ch. 7.7 - Prob. 1CFU Ch. 7.7 - Prob. 2CFU Ch. 7.7 - Prob. 3CFU Ch. 7.7 - Prob. 4CFU Ch. 7.7 - Prob. 5CFU Ch. 7.7 - Prob. 6CFU Ch. 7.7 - Prob. 7CFU Ch. 7.7 - Prob. 8CFU Ch. 7.7 - Prob. 9CFU Ch. 7.7 - Prob. 10CFU Ch. 7.7 - Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - Prob. 14E Ch. 7.7 - Prob. 15E Ch. 7.7 - Prob. 16E Ch. 7.7 - Prob. 17E Ch. 7.7 - Prob. 18E Ch. 7.7 - Prob. 19E Ch. 7.7 - Prob. 20E Ch. 7.7 - Prob. 21E Ch. 7.7 - Prob. 22E Ch. 7.7 - Prob. 23E Ch. 7.7 - Prob. 24E Ch. 7.7 - Prob. 25E Ch. 7.7 - Prob. 26E Ch. 7.7 - Prob. 27E Ch. 7.7 - Prob. 28E Ch. 7.7 - Prob. 29E Ch. 7.7 - Prob. 30E Ch. 7.7 - Prob. 31E Ch. 7.7 - Prob. 32E Ch. 7.7 - Prob. 33E Ch. 7.7 - Prob. 34E Ch. 7.7 - Prob. 35E Ch. 7.7 - Prob. 36E Ch. 7.7 - Prob. 37E Ch. 7.7 - Prob. 38E Ch. 7.7 - Prob. 39E Ch. 7.7 - Prob. 40E Ch. 7 - Prob. 1SGA Ch. 7 - Prob. 2SGA Ch. 7 - Prob. 3SGA Ch. 7 - Prob. 4SGA Ch. 7 - Prob. 5SGA Ch. 7 - Prob. 6SGA Ch. 7 - Prob. 7SGA Ch. 7 - Prob. 8SGA Ch. 7 - Prob. 9SGA Ch. 7 - Prob. 10SGA Ch. 7 - Prob. 11SGA Ch. 7 - Prob. 12SGA Ch. 7 - Prob. 13SGA Ch. 7 - Prob. 14SGA Ch. 7 - Prob. 15SGA Ch. 7 - Prob. 16SGA Ch. 7 - Prob. 17SGA Ch. 7 - Prob. 18SGA Ch. 7 - Prob. 19SGA Ch. 7 - Prob. 20SGA Ch. 7 - Prob. 21SGA Ch. 7 - Prob. 22SGA Ch. 7 - Prob. 23SGA Ch. 7 - Prob. 24SGA Ch. 7 - Prob. 25SGA Ch. 7 - Prob. 26SGA Ch. 7 - Prob. 27SGA Ch. 7 - Prob. 28SGA Ch. 7 - Prob. 29SGA Ch. 7 - Prob. 30SGA Ch. 7 - Prob. 31SGA Ch. 7 - Prob. 32SGA Ch. 7 - Prob. 33SGA Ch. 7 - Prob. 34SGA Ch. 7 - Prob. 35SGA Ch. 7 - Prob. 36SGA Ch. 7 - Prob. 37SGA Ch. 7 - Prob. 38SGA Ch. 7 - Prob. 39SGA Ch. 7 - Prob. 40SGA Ch. 7 - Prob. 41SGA Ch. 7 - Prob. 42SGA Ch. 7 - Prob. 43SGA Ch. 7 - Prob. 44SGA Ch. 7 - Prob. 45SGA Ch. 7 - Prob. 46SGA Ch. 7 - Prob. 47SGA Ch. 7 - Prob. 1SAP Ch. 7 - Prob. 2SAP Ch. 7 - Prob. 3SAP Ch. 7 - Prob. 4SAP Ch. 7 - Prob. 5SAP Ch. 7 - Prob. 6SAP Ch. 7 - Prob. 7SAP Ch. 7 - Prob. 8SAP Ch. 7 - Prob. 9SAP Ch. 7 - Prob. 10SAP

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