Trigonometry Examples

$(\frac{4 \sqrt{3}}{7}, \frac{1}{7})$

Step 1

To find the $\cot (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{4 \sqrt{3}}{7}, \frac{1}{7})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{4 \sqrt{3}}{7}, 0)$ , and $(\frac{4 \sqrt{3}}{7}, \frac{1}{7})$ .

Opposite : $\frac{1}{7}$

Adjacent : $\frac{4 \sqrt{3}}{7}$

Step 2

$\cot (θ) = \frac{Adjacent}{Opposite}$ therefore $\cot (θ) = \frac{\frac{4 \sqrt{3}}{7}}{\frac{1}{7}}$ .

$\frac{\frac{4 \sqrt{3}}{7}}{\frac{1}{7}}$

Step 3

Simplify $\cot (θ)$ .

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\cot (θ) = \frac{4 \sqrt{3}}{7} \cdot 7$

Step 3.2

Cancel the common factor of $7$ .

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Step 3.2.1

Cancel the common factor.

$\cot (θ) = \frac{4 \sqrt{3}}{7} \cdot 7$

Step 3.2.2

Rewrite the expression.

$\cot (θ) = 4 \sqrt{3}$

Step 4

Approximate the result.

$\cot (θ) = 4 \sqrt{3} \approx 6.92820323$