Q. 96 solve each equation on the inter... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 96 (page 487)

solve each equation on the interval $0 鈮� 胃 < 2 蟺$
$c o t 胃 + c s c 胃 = - \sqrt{3}$

Short Answer

Expert verified

The solution of $c o t 胃 + c s c 胃 = - \sqrt{3}$ in interval $0 鈮� 胃 < 2 蟺$ is $胃 = \frac{5 蟺}{3}$

Step by step solution

Step 1. Given data

The given equation is

$c o t 胃 + c s c 胃 = - \sqrt{3}$

The given interval is

$0 鈮� 胃 < 2 蟺$

Step 2. Formation of the proper equation

Rearrange the equation

$c o t 胃 + c s c 胃 = - \sqrt{3} \frac{\cos 胃}{\sin 胃} + \frac{1}{\sin 胃} = - \sqrt{3} \cos 胃 + 1 = - \sqrt{3} \sin 胃 \cos 胃 + \sqrt{3} \sin 胃 = - 1 \frac{1}{2} \cos 胃 + \frac{\sqrt{3}}{2} \sin 胃 = - \frac{1}{2}$

Step 3. Use of sum formula of sin function

Rearrange the equation and use the sum formula of the sine function

$\frac{1}{2} \cos 胃 + \frac{\sqrt{3}}{2} \sin 胃 = - \frac{1}{2} S i n \frac{蟺}{6} 路 \cos 胃 + \cos \frac{蟺}{6} 路 \sin 胃 = S i n \frac{7 蟺}{6} \sin (\frac{蟺}{6} + 胃) = S i n \frac{7 蟺}{6} \frac{蟺}{6} + 胃 = \frac{7 蟺}{6} 胃 = 蟺$

But the equation is not true for $胃 = 蟺$ so it is not the solution

Step 4. Use of sum formula of sin function

Rearrange the equation and use the sum formula of the sine function

$\frac{1}{2} \cos 胃 + \frac{\sqrt{3}}{2} \sin 胃 = - \frac{1}{2} S i n \frac{蟺}{6} 路 \cos 胃 + \cos \frac{蟺}{6} 路 \sin 胃 = S i n \frac{11 蟺}{6} \sin (\frac{蟺}{6} + 胃) = S i n \frac{11 蟺}{6} \frac{蟺}{6} + 胃 = \frac{11 蟺}{6} 胃 = \frac{10 蟺}{6} 胃 = \frac{5 蟺}{3}$

The equation is true for $胃 = \frac{5 蟺}{3}$

so solution is $胃 = \frac{5 蟺}{3}$

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91影视

solve each equation on the interval $0 鈮� 胃 < 2 蟺$
$c o t 胃 + c s c 胃 = - \sqrt{3}$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Formation of the proper equation

Step 3. Use of sum formula of sin function

Step 4. Use of sum formula of sin function

One App. One Place for Learning.

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91影视

solve each equation on the interval 0鈮�胃<2蟺cot胃+csc胃=-3

Short Answer

Step by step solution

Step 1. Given data

Step 2. Formation of the proper equation

Step 3. Use of sum formula of sin function

Step 4. Use of sum formula of sin function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Applied Mathematics

Mechanics Maths

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

solve each equation on the interval $0 鈮� 胃 < 2 蟺$
$c o t 胃 + c s c 胃 = - \sqrt{3}$