Chapter 7: Q. 72 (page 496)

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

Short Answer

Expert verified

The solution set for the equation $\sin (2 θ) = \cos θ$ is, $\{\frac{π}{6}, \frac{π}{2}, \frac{5 π}{6}, \frac{3 π}{2}\}$ .

Step by step solution

Step 1 Given equation is,

$\sin (2 θ) = \cos θ$ .

The double angle formula for $\sin (2 θ)$ is $\sin (2 θ) = 2 \sin θ \cos θ$ .

Substitute the known values in the given equation.

$2 \sin θ \cos θ = \cos θ 2 \sin θ \cos θ - \cos θ = 0 \cos θ (2 \sin θ - 1) = 0 \cos θ = 0 o r 2 \sin θ - 1 = 0 2 \sin θ = 1 \sin θ = \frac{1}{2}$

Step 2 Solving each equation in the interval [0,2π),

$θ = \frac{π}{6} θ = \frac{π}{2} θ = \frac{5 π}{6} θ = \frac{3 π}{2}$

Hence the solution set is, $\{\frac{π}{6}, \frac{π}{2}, \frac{5 π}{6}, \frac{3 π}{2}\}$ .

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

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Solving each equation in the interval [0,2π),

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In Problems 69-78, solve each equation on the interval 0≤θ<2π.sin2θ=cosθ.

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Solving each equation in the interval [0,2π),

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Applied Mathematics

Pure Maths

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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