Trigonometry Examples

$\tan (θ) = \frac{4}{3}$

Step 1

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

$θ = \arctan (\frac{4}{3})$

Step 2

Simplify the right side.

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Step 2.1

Evaluate $\arctan (\frac{4}{3})$ .

$θ = 53.13010235$

Step 3

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.

$θ = 180 + 53.13010235$

Step 4

Add $180$ and $53.13010235$ .

$θ = 233.13010235$

Step 5

Find the period of $\tan (θ)$ .

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

$\frac{180}{1}$

Step 5.4

Divide $180$ by $1$ .

$180$

Step 6

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

$θ = 53.13010235 + 180 n, 233.13010235 + 180 n$ , for any integer $n$

Step 7

Consolidate the answers.

$θ = 53.13010235 + 180 n$ , for any integer $n$