Precalculus Examples

$(\frac{2}{9}, \frac{\sqrt{77}}{9})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{2}{9}, \frac{\sqrt{77}}{9})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{2}{9}, 0)$ , and $(\frac{2}{9}, \frac{\sqrt{77}}{9})$ .

Opposite : $\frac{\sqrt{77}}{9}$

Adjacent : $\frac{2}{9}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{\sqrt{77}}{9}}{\frac{2}{9}}$ .

$\frac{\frac{\sqrt{77}}{9}}{\frac{2}{9}}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{\sqrt{77}}{9} \cdot \frac{9}{2}$

Step 3.2

Cancel the common factor of $9$ .

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Step 3.2.1

Cancel the common factor.

$\tan (θ) = \frac{\sqrt{77}}{9} \cdot \frac{9}{2}$

Step 3.2.2

Rewrite the expression.

$\tan (θ) = \sqrt{77} (\frac{1}{2})$

Step 3.3

Combine $\sqrt{77}$ and $\frac{1}{2}$ .

$\tan (θ) = \frac{\sqrt{77}}{2}$

Step 4

Approximate the result.

$\tan (θ) = \frac{\sqrt{77}}{2} \approx 4.38748219$