Chapter 7: Q. 78 (page 496)

In Problems $69 - 78$ , solve each equation on the interval $0 \leq θ < 2 π$
$\tan (2 θ) + 2 \cos θ = 0$

Short Answer

Expert verified

The solution set is $θ \in \{\frac{π}{2}, \frac{7 π}{6}, \frac{3 π}{2}, \frac{11 π}{6}\}$

Step by step solution

Given information

Given function $\tan (2 θ) + 2 \cos θ = 0$

Simplifying the equation

Simplifying, we get

$\tan (2 θ) + 2 \cos θ = 0 \frac{\sin (2 θ)}{\cos (2 θ)} + 2 \cos θ = 0 \sin (2 θ) + 2 \cos θ \cos (2 θ) = 0 2 \sin θ \cos θ + 2 \cos θ (1 - 2 \sin^{2} θ) = 0$

Solving further

Solving, we get

$2 \cos θ (\sin θ + 1 - 2 \sin^{2} θ) = 0 \cos θ (2 \sin^{2} θ - \sin θ - 1) = 0 \cos θ (2 \sin θ + 1) (\sin θ - 1) = 0 \cos θ = 0 \sin θ = - \frac{1}{2} θ = \frac{π}{2} θ = \frac{3 π}{2} θ = \frac{7 π}{6} θ = \frac{11 π}{6} θ = \frac{π}{2}$

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In Problems $69 - 78$ , solve each equation on the interval $0 \leq θ < 2 π$
$\tan (2 θ) + 2 \cos θ = 0$

Short Answer

Step by step solution

Given information

Simplifying the equation

Solving further

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In Problems 69-78, solve each equation on the interval 0≤θ<2πtan(2θ)+2cosθ=0

Short Answer

Step by step solution

Given information

Simplifying the equation

Solving further

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems $69 - 78$ , solve each equation on the interval $0 \leq θ < 2 π$
$\tan (2 θ) + 2 \cos θ = 0$