Precalculus Examples

$(- \frac{1}{3}, \frac{2 \sqrt{2}}{3})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- \frac{1}{3}, \frac{2 \sqrt{2}}{3})$ , draw the triangle between the three points $(0, 0)$ , $(- \frac{1}{3}, 0)$ , and $(- \frac{1}{3}, \frac{2 \sqrt{2}}{3})$ .

Opposite : $\frac{2 \sqrt{2}}{3}$

Adjacent : $- \frac{1}{3}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{2 \sqrt{2}}{3}}{- \frac{1}{3}}$ .

$\frac{\frac{2 \sqrt{2}}{3}}{- \frac{1}{3}}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{2 \sqrt{2}}{3} \cdot (- 1 \cdot 3)$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Factor $3$ out of $- 1 \cdot 3$ .

$\tan (θ) = \frac{2 \sqrt{2}}{3} \cdot (3 \cdot - 1)$

Step 3.2.2

Cancel the common factor.

$\tan (θ) = \frac{2 \sqrt{2}}{3} \cdot (3 \cdot - 1)$

Step 3.2.3

Rewrite the expression.

$\tan (θ) = 2 \sqrt{2} \cdot - 1$

Step 3.3

Multiply $- 1$ by $2$ .

$\tan (θ) = - 2 \sqrt{2}$

Step 4

Approximate the result.

$\tan (θ) = - 2 \sqrt{2} \approx - 2.82842712$