# How do you solve 2 cos(x) = sqrt(3)?

## Question:

How do you solve 2 cos(x) = sqrt(3)?

## Trigonometric Angles and Ratios:

In mathematics, basic trigonometric ratios are defined as those functions in which the angles of a right triangle (acute angles) are related to the lengths of two sides of the triangle.

The trigonometric ratio of cosine in a right triangle of acute angle {eq}\theta {/eq} is given by:

$$\cos \theta = \frac{\text{adjacent side length}}{\text{length of the hypotenuse}}$$

The values of some standard angles of trigonometric ratios are as follows:

\begin{align} \sin 45^{\circ} &= \cos 45^{\circ} = \frac{1}{\sqrt{2}} \\[0.2cm] \tan 45^{\circ} &= \cot 45^{\circ} = 1 \\[0.2cm] \cos 30^{\circ} &= \sin 60^{\circ} = \frac{\sqrt{3}}{2} \\[0.2cm] \sin 0^{\circ} &= \cos 90^{\circ} = 0 \\[0.2cm] \end{align}

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We are given the trigonometric equation:

$$2 \cos (x) = \sqrt{3}$$

We separate the trigonometric ratio of cosine from all the constants:

\begin...