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Chapter 5: Problem 14

Solve the equation. $$3 \sin x+1=\sin x$$

Short Answer

Expert verified
The solutions to the equation are \(x = 7\pi/6\) and \(x = 11\pi/6\).

Step by step solution

01

- Rewrite the equation

Begin by rewriting the given equation as follows: \(3 \sin x - \sin x = -1 \)
02

- Combine similar terms

Combine the terms related to the sine of x to simplify the equation: \(2 \sin x = -1 \)
03

- Solve for \(\sin x\)

Solve the equation for \(\sin x\) by dividing both sides of the equation by 2: \(\sin x = -\frac{1}{2} \)
04

- Find \(x\)

Since the sine of certain specific angles are well known, observe that \(\sin x = -\frac{1}{2} \) corresponds to \(x = 7\pi/6\) and \(x = 11\pi/6\) in the interval of \([0, 2\pi]\).

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Most popular questions from this chapter

Write the expression as the sine, cosine, or tangent of an angle. $$\cos 3 x \cos 2 y+\sin 3 x \sin 2 y$$

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Find all solutions of the equation in the interval \([0,2 \pi) .\) Use a graphing utility to graph the equation and verify the solutions. $$\sin \frac{x}{2}+\cos x=0$$

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Prove the identity. $$\sin \left(\frac{\pi}{2}+x\right)=\cos x$$
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