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

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

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Step 3.1

Factor $2$ out of $8$ .

$\tan (θ) = \frac{2 (4)}{6}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\tan (θ) = \frac{4}{3}$

Step 4

Approximate the result.

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