Solve for X in Degrees tan(X)=2

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Trigonometry

$\tan (X) = 2$

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

$X = \arctan (2)$

Simplify the right side.

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Evaluate $\arctan (2)$ .

$X = 63.43494882$

The tangent function is positive in the first and third quadrants. To find the second solution, subtract the reference angle from $180$ to find the solution in the fourth quadrant.

$X = 180 + 63.43494882$

Add $180$ and $63.43494882$ .

$X = 243.43494882$

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

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The period of the function can be calculated using $\frac{180}{| b |}$ .

$\frac{180}{| b |}$

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

$\frac{180}{| 1 |}$

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

$\frac{180}{1}$

Divide $180$ by $1$ .

$180$

The period of the $\tan (X)$ function is $180$ so values will repeat every $180$ degrees in both directions.

$X = 63.43494882 + 180 n, 243.43494882 + 180 n$ , for any integer $n$

Consolidate the answers.

$X = 63.43494882 + 180 n$ , for any integer $n$

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