Trigonometry Examples

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

Step 1

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

Opposite : $2 \sqrt{3}$

Adjacent : $- 2$

Step 2

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

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

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Cancel the common factor of $2$ and $- 2$ .

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Step 3.1.1

Factor $2$ out of $2 \sqrt{3}$ .

$\tan (θ) = \frac{2 (\sqrt{3})}{- 2}$

Step 3.1.2

Move the negative one from the denominator of $\frac{\sqrt{3}}{- 1}$ .

$\tan (θ) = - 1 \cdot \sqrt{3}$

Step 3.2

Rewrite $- 1 \cdot \sqrt{3}$ as $- \sqrt{3}$ .

$\tan (θ) = - \sqrt{3}$

Step 4

Approximate the result.

$\tan (θ) = - \sqrt{3} \approx - 1.7320508$