Trigonometry Examples

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

Step 1

Divide $73.7$ by $39.4$ .

$\tan (A) = 1.87055837$

Step 2

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

$A = \arctan (1.87055837)$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Evaluate $\arctan (1.87055837)$ .

$A = 61.87105211$

Step 4

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.

$A = 180 + 61.87105211$

Step 5

Add $180$ and $61.87105211$ .

$A = 241.87105211$

Step 6

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

Tap for more steps...

Step 6.1

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

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

Step 6.2

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

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

Step 6.3

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

$\frac{180}{1}$

Step 6.4

Divide $180$ by $1$ .

$180$

Step 7

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 $n$

Step 8

Consolidate the answers.

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