Solve for a tan(a)=4

$\tan (a) = 4$

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

$a = \arctan (4)$

Simplify the right side.

Evaluate $\arctan (4)$ .

$a = 1.32581766$

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.

$a = (3.14159265) + 1.32581766$

Solve for $a$ .

Remove parentheses.

$a = 3.14159265 + 1.32581766$

Remove parentheses.

$a = (3.14159265) + 1.32581766$

Add $3.14159265$ and $1.32581766$ .

$a = 4.46741031$

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

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 $\tan (a)$ function is $π$ so values will repeat every $π$ radians in both directions.

$a = 1.32581766 + π n, 4.46741031 + π n$ , for any integer $n$

Consolidate $1.32581766 + π n$ and $4.46741031 + π n$ to $1.32581766 + π n$ .

$a = 1.32581766 + π n$ , for any integer $n$

Solve for a tan(a)=4

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