Trigonometry Examples

$(- \frac{4}{5}, - \frac{3}{5})$

Step 1

To find the $\cot (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- \frac{4}{5}, - \frac{3}{5})$ , draw the triangle between the three points $(0, 0)$ , $(- \frac{4}{5}, 0)$ , and $(- \frac{4}{5}, - \frac{3}{5})$ .

Opposite : $- \frac{3}{5}$

Adjacent : $- \frac{4}{5}$

Step 2

$\cot (θ) = \frac{Adjacent}{Opposite}$ therefore $\cot (θ) = \frac{- \frac{4}{5}}{- \frac{3}{5}}$ .

$\frac{- \frac{4}{5}}{- \frac{3}{5}}$

Step 3

Simplify $\cot (θ)$ .

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Step 3.1

Dividing two negative values results in a positive value.

$\cot (θ) = \frac{\frac{4}{5}}{\frac{3}{5}}$

Step 3.2

Multiply the numerator by the reciprocal of the denominator.

$\cot (θ) = \frac{4}{5} \cdot \frac{5}{3}$

Step 3.3

Cancel the common factor of $5$ .

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Step 3.3.1

Cancel the common factor.

$\cot (θ) = \frac{4}{5} \cdot \frac{5}{3}$

Step 3.3.2

Rewrite the expression.

$\cot (θ) = 4 (\frac{1}{3})$

Step 3.4

Combine $4$ and $\frac{1}{3}$ .

$\cot (θ) = \frac{4}{3}$

Step 4

Approximate the result.

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