Trigonometry Examples

$(12, - 9)$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(12, - 9)$ , draw the triangle between the three points $(0, 0)$ , $(12, 0)$ , and $(12, - 9)$ .

Opposite : $- 9$

Adjacent : $12$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{- 9}{12}$ .

$\frac{- 9}{12}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Cancel the common factor of $- 9$ and $12$ .

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Step 3.1.1

Factor $3$ out of $- 9$ .

$\tan (θ) = \frac{3 (- 3)}{12}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $3$ out of $12$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

$\tan (θ) = \frac{- 3}{4}$

Step 3.2

Move the negative in front of the fraction.

$\tan (θ) = - \frac{3}{4}$

Step 4

Approximate the result.

$\tan (θ) = - \frac{3}{4} \approx - 0.75$