Trigonometry Examples

$(\frac{3}{8}, \frac{\sqrt{55}}{8})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{3}{8}, \frac{\sqrt{55}}{8})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{3}{8}, 0)$ , and $(\frac{3}{8}, \frac{\sqrt{55}}{8})$ .

Opposite : $\frac{\sqrt{55}}{8}$

Adjacent : $\frac{3}{8}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{\sqrt{55}}{8}}{\frac{3}{8}}$ .

$\frac{\frac{\sqrt{55}}{8}}{\frac{3}{8}}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{\sqrt{55}}{8} \cdot \frac{8}{3}$

Step 3.2

Cancel the common factor of $8$ .

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Step 3.2.1

Cancel the common factor.

$\tan (θ) = \frac{\sqrt{55}}{8} \cdot \frac{8}{3}$

Step 3.2.2

Rewrite the expression.

$\tan (θ) = \sqrt{55} (\frac{1}{3})$

Step 3.3

Combine $\sqrt{55}$ and $\frac{1}{3}$ .

$\tan (θ) = \frac{\sqrt{55}}{3}$

Step 4

Approximate the result.

$\tan (θ) = \frac{\sqrt{55}}{3} \approx 2.47206616$