Chapter 7: Q. 71 (page 504)

In Problems 64-75, solve each equation on the interval $0 \leq θ < 2 π$

Short Answer

Expert verified

The solution set is $θ \in \{0, \frac{π}{6}, \frac{5 π}{6}\}$

Step by step solution

Given information

Given expression $\sin (2 θ) - \cos θ - 2 \sin θ + 1 = 0$

Checking the value lie in the specific interval

Calculating, we get

$\sin (2 θ) - \cos θ - 2 \sin θ + 1 = 0 2 \sin θ \cos θ - \cos θ - 2 \sin θ + 1 = 0 2 \sin θ (\cos θ - 1) - (\cos θ - 1) = 0 (\cos θ - 1) (2 \sin θ - 1) = 0 \cos θ - 1 = 0 \cos θ = 1 2 \sin θ - 1 = 0 2 \sin θ = 1 \sin θ = \frac{1}{2} θ \in \{0, \frac{π}{6}, \frac{5 π}{6}\}$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 64-75, solve each equation on the interval $0 \leq θ < 2 π$

Short Answer

Step by step solution

Given information

Checking the value lie in the specific interval

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Pure Maths

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 64-75, solve each equation on the interval0≤θ<2π

Short Answer

Step by step solution

Given information

Checking the value lie in the specific interval

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Pure Maths

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 64-75, solve each equation on the interval $0 \leq θ < 2 π$