Chapter 7: Q. 29 (page 505)

Solve each equation on $0 \leq θ < 2 π$ .
$4 \sin^{2} θ + 7 \sin θ = 2$

Short Answer

Expert verified

The solutions are $θ = \{0.253, 2.889\}$ .

Step by step solution

Step 1. Given Information

We are given the equation $4 \sin^{2} θ + 7 \sin θ = 2$ and we need to find the solutions of the equation on the interval $0 \leq θ < 2 π$ .

Step 2. Simplifying the equation

Factorizing the equation we get,

$4 \sin^{2} θ + 7 \sin θ = 2 \Rightarrow 4 \sin^{2} θ + 7 \sin θ - 2 = 0 \Rightarrow 4 \sin^{2} θ + 8 \sin θ - \sin θ - 2 = 0 \Rightarrow 4 \sin θ (\sin θ + 2) - 1 (\sin θ + 2) = 0 \Rightarrow (4 \sin θ - 1) (\sin θ + 2) = 0$

Step 3. Finding the solutions

When

$(4 \sin θ - 1) = 0 \Rightarrow 4 \sin θ = 1 \Rightarrow \sin θ = \frac{1}{4}$

In the interval $[0, 2 π)$ , $θ = {0.253, 2.889}$ .

When

$\sin θ + 2 = 0 \Rightarrow \sin θ = - 2$

Since value of $θ$ ranges between $0$ and $1$ in this interval. There is no solution for $θ$ when $\sin θ = - 2$

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Solve each equation on $0 \leq θ < 2 π$ .
$4 \sin^{2} θ + 7 \sin θ = 2$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplifying the equation

Step 3. Finding the solutions

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Solve each equation on 0≤θ<2π.4sin2θ+7sinθ=2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplifying the equation

Step 3. Finding the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation on $0 \leq θ < 2 π$ .
$4 \sin^{2} θ + 7 \sin θ = 2$