/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 Solve the equation. $$\sqrt{3}... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 13

Solve the equation. $$\sqrt{3} \csc x-2=0$$

Short Answer

Expert verified
The solution to the equation \(\sqrt{3} \csc x - 2 = 0\) is \(x = \pi/3, 2\pi/3\)

Step by step solution

01

Rewrite the equation

First, define the equation which we aim to solve: \(\sqrt{3} \csc x - 2 = 0\). We can rewrite the equation with the csc x term isolated: \(\csc x = 2/\sqrt{3}\)
02

Convert csc to sin

Recall the reciprocal identity that \(\csc x = 1/\sin x\). Therefore, we can say \(1/\sin x = 2/\sqrt{3}\) or \(\sin x = \sqrt{3}/2\)
03

Solve for x

Knowing that \(\sin x = \sqrt{3}/2\), we must identify the angles for which this is true. In the first and second quadrants \(x = \pi/3, 2\pi/3\)

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