Solve for a in Degrees tan(a)=73.7/39.4

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Trigonometry

$\tan (a) = \frac{73.7}{39.4}$

Divide $73.7$ by $39.4$ .

$\tan (a) = 1.87055837$

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

$a = \arctan (1.87055837)$

Simplify the right side.

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Evaluate $\arctan (1.87055837)$ .

$a = 61.87105211$

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.

$a = 180 + 61.87105211$

Add $180$ and $61.87105211$ .

$a = 241.87105211$

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

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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 $\tan (a)$ function is $180$ so values will repeat every $180$ degrees in both directions.

$a = 61.87105211 + 180 n, 241.87105211 + 180 n$ , for any integer $n$

Consolidate the answers.

$a = 61.87105211 + 180 n$ , for any integer $n$

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