Trigonometry Examples

$(\frac{1}{2}, \frac{\sqrt{3}}{3})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{1}{2}, \frac{\sqrt{3}}{3})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{1}{2}, 0)$ , and $(\frac{1}{2}, \frac{\sqrt{3}}{3})$ .

Opposite : $\frac{\sqrt{3}}{3}$

Adjacent : $\frac{1}{2}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{\sqrt{3}}{3}}{\frac{1}{2}}$ .

$\frac{\frac{\sqrt{3}}{3}}{\frac{1}{2}}$

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

Combine $\frac{\sqrt{3}}{3}$ and $2$ .

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

Step 3.3

Move $2$ to the left of $\sqrt{3}$ .

$\tan (θ) = \frac{2 \sqrt{3}}{3}$

Step 4

Approximate the result.

$\tan (θ) = \frac{2 \sqrt{3}}{3} \approx 1.15470053$