Trigonometry Examples

$(8, 4)$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(8, 4)$ , draw the triangle between the three points $(0, 0)$ , $(8, 0)$ , and $(8, 4)$ .

Opposite : $4$

Adjacent : $8$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{4}{8}$ .

$\frac{4}{8}$

Step 3

Cancel the common factor of $4$ and $8$ .

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Step 3.1

Factor $4$ out of $4$ .

$\tan (θ) = \frac{4 (1)}{8}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $8$ .

$\tan (θ) = \frac{4 \cdot 1}{4 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$\tan (θ) = \frac{4 \cdot 1}{4 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$\tan (θ) = \frac{1}{2}$

Step 4

Approximate the result.

$\tan (θ) = \frac{1}{2} \approx 0.5$