Trigonometry Examples

$(- 6, 8)$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- 6, 8)$ , draw the triangle between the three points $(0, 0)$ , $(- 6, 0)$ , and $(- 6, 8)$ .

Opposite : $8$

Adjacent : $- 6$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{8}{- 6}$ .

$\frac{8}{- 6}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Cancel the common factor of $8$ and $- 6$ .

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Step 3.1.1

Factor $2$ out of $8$ .

$\tan (θ) = \frac{2 (4)}{- 6}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $- 6$ .

$\tan (θ) = \frac{2 \cdot 4}{2 \cdot - 3}$

Step 3.1.2.2

Cancel the common factor.

$\tan (θ) = \frac{2 \cdot 4}{2 \cdot - 3}$

Step 3.1.2.3

Rewrite the expression.

$\tan (θ) = \frac{4}{- 3}$

Step 3.2

Move the negative in front of the fraction.

$\tan (θ) = - \frac{4}{3}$

Step 4

Approximate the result.

$\tan (θ) = - \frac{4}{3} \approx - 1.\overline{3}$