Solve for x in Radians tan(x)=( square root of 3)/2

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Trigonometry

$\tan (x) = \frac{\sqrt{3}}{2}$

Take the inverse tangent of both sides of the equation to extract $x$ from inside the tangent.

$x = \arctan (\frac{\sqrt{3}}{2})$

Simplify the right side.

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Evaluate $\arctan (\frac{\sqrt{3}}{2})$ .

$x = 0.71372437$

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from $π$ to find the solution in the fourth quadrant.

$x = (3.14159265) + 0.71372437$

Solve for $x$ .

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Remove parentheses.

$x = 3.14159265 + 0.71372437$

Remove parentheses.

$x = (3.14159265) + 0.71372437$

Add $3.14159265$ and $0.71372437$ .

$x = 3.85531703$

Find the period of $\tan (x)$ .

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The period of the function can be calculated using $\frac{π}{| b |}$ .

$\frac{π}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{π}{1}$

Divide $π$ by $1$ .

$π$

The period of the $\tan (x)$ function is $π$ so values will repeat every $π$ radians in both directions.

$x = 0.71372437 + π n, 3.85531703 + π n$ , for any integer $n$

Consolidate the answers.

$x = 0.71372437 + π n$ , for any integer $n$

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