Q. 33 In Problems 11鈥�34, solve each ... [FREE SOLUTION]

Chapter 7: Q. 33 (page 465)

In Problems 11鈥�34, solve each equation on the interval $0 鈮� 胃鈮� 2 蟺$
role="math" localid="1646668881995" $\tan (\frac{胃}{2} + \frac{蟺}{3}) = 1$

Short Answer

Expert verified

The solution set is $\{\frac{11 蟺}{6}\}$

Step by step solution

Step 1. Given Information

In the given problem we have to solve each equation on the interval $0 鈮� 胃鈮� 2 蟺$

$\tan (\frac{胃}{2} + \frac{蟺}{3}) = 1$

Step 2. In the interval [0,2π), the tangent function 1 equals at src="data:image/svg+xml;base64,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" role="math" localid="1646668970256" src="https://studysmarter-mediafiles.s3.amazonaws.com/media/textbook-exercise-images/3adf2e17-9ef7-4f1b-816b-a6429a81a9c7.svg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIA4OLDUDE42UZHAIET%2F20220307%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20220307T161229Z&X-Amz-Expires=90000&X-Amz-SignedHeaders=host&X-Amz-Signature=7e11053f7ed50a5f4c0c9b0c412628eb4bec4560798224531fc62c3ea80dba2f" π4

So, we know that $\frac{胃}{2} + \frac{蟺}{3}$ must equal $\frac{蟺}{4}$ .

To find these solutions, write the general formula that gives all the solutions.

role="math" localid="1646669186320" $\frac{胃}{2} + \frac{蟺}{3} = \frac{蟺}{4} + 蟺苍$

Subtract by $\frac{蟺}{3}$ on both side

role="math" localid="1646669323651" $\frac{胃}{2} + \frac{蟺}{3} - \frac{蟺}{3} = \frac{蟺}{4} + 蟺苍 - \frac{蟺}{3} \frac{胃}{2} = \frac{蟺}{4} 路 \frac{3}{3} + 蟺苍路 \frac{12}{12} - \frac{蟺}{3} 路 \frac{4}{4} \frac{胃}{2} = \frac{3 蟺}{12} + \frac{12 蟺苍}{12} - \frac{4 蟺}{12} \frac{胃}{2} = \frac{3 蟺 + 12 蟺苍 - 4 蟺}{12} \frac{胃}{2} = \frac{12 蟺苍 - 蟺}{12} \frac{胃}{2} 脳 2 = \frac{12 蟺苍 - 蟺}{12} 脳 2 胃 = \frac{12 蟺苍 - 蟺}{6}$

Step 3. The general formula is θ=12πn-π6

So the value of given function in interval $[0, 2 蟺)$ is

$胃 = \frac{12 蟺脳 1 - 蟺}{6} 胃 = \frac{12 蟺 - 蟺}{6} 胃 = \frac{11 蟺}{6}$

So the solution set is $\{\frac{11 蟺}{6}\}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

91影视

In Problems 11鈥�34, solve each equation on the interval $0 鈮� 胃鈮� 2 蟺$
role="math" localid="1646668881995" $\tan (\frac{胃}{2} + \frac{蟺}{3}) = 1$

Short Answer

Step by step solution

Step 1. Given Information

Step 3. The general formula is θ=12πn-π6

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Calculus

Pure Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

91影视

In Problems 11鈥�34, solve each equation on the interval 0鈮�胃鈮�2蟺role="math" localid="1646668881995" tan胃2+蟺3=1

Short Answer

Step by step solution

Step 1. Given Information

Step 3. The general formula is θ=12πn-π6

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Calculus

Pure Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

In Problems 11鈥�34, solve each equation on the interval $0 鈮� 胃鈮� 2 蟺$
role="math" localid="1646668881995" $\tan (\frac{胃}{2} + \frac{蟺}{3}) = 1$