Trigonometry Examples

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

Step 1

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

Opposite : $\frac{\sqrt{3}}{2}$

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

Step 2

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

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

Step 3

Simplify $\tan (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$\tan (θ) = \sqrt{3}$

Step 4

Approximate the result.

$\tan (θ) = \sqrt{3} \approx 1.7320508$