Solve for x tan(x)=5/6

$\tan (x) = \frac{5}{6}$

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

$x = \arctan (\frac{5}{6})$

Evaluate $\arctan (\frac{5}{6})$ .

$x = 0.69473827$

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.

$x = (3.14159265) + 0.69473827$

Simplify the expression to find the second solution.

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Remove the parentheses around the expression $3.14159265$ .

$x = 3.14159265 + 0.69473827$

Add $3.14159265$ and $0.69473827$ .

$x = 3.83633092$

Find the period.

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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.

$\frac{π}{| 1 |}$

Solve the equation.

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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.

$x = 0.69473827 + π n, 3.83633092 + π n$ , for any integer $n$

Consolidate the answers.

$x = 0.69473827 + π n$ , for any integer $n$

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