Trigonometry Examples

$(4, - 6)$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(4, - 6)$ , draw the triangle between the three points $(0, 0)$ , $(4, 0)$ , and $(4, - 6)$ .

Opposite : $- 6$

Adjacent : $4$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{- 6}{4}$ .

$\frac{- 6}{4}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Cancel the common factor of $- 6$ and $4$ .

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Step 3.1.1

Factor $2$ out of $- 6$ .

$\tan (θ) = \frac{2 (- 3)}{4}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $4$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

$\tan (θ) = \frac{- 3}{2}$

Step 3.2

Move the negative in front of the fraction.

$\tan (θ) = - \frac{3}{2}$

Step 4

Approximate the result.

$\tan (θ) = - \frac{3}{2} \approx - 1.5$