Trigonometry Examples

$(- 10, 24)$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- 10, 24)$ , draw the triangle between the three points $(0, 0)$ , $(- 10, 0)$ , and $(- 10, 24)$ .

Opposite : $24$

Adjacent : $- 10$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{24}{- 10}$ .

$\frac{24}{- 10}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Cancel the common factor of $24$ and $- 10$ .

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Step 3.1.1

Factor $2$ out of $24$ .

$\tan (θ) = \frac{2 (12)}{- 10}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $2$ out of $- 10$ .

$\tan (θ) = \frac{2 \cdot 12}{2 \cdot - 5}$

Step 3.1.2.2

Cancel the common factor.

$\tan (θ) = \frac{2 \cdot 12}{2 \cdot - 5}$

Step 3.1.2.3

Rewrite the expression.

$\tan (θ) = \frac{12}{- 5}$

Step 3.2

Move the negative in front of the fraction.

$\tan (θ) = - \frac{12}{5}$

Step 4

Approximate the result.

$\tan (θ) = - \frac{12}{5} \approx - 2.4$