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

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2

Cancel the common factor of $5$ .

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Step 3.2.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

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

Step 3.2.2

Factor $5$ out of $- 5$ .

$\cot (θ) = \frac{4}{5} \cdot \frac{5 (- 1)}{3}$

Step 3.2.3

Cancel the common factor.

$\cot (θ) = \frac{4}{5} \cdot \frac{5 \cdot - 1}{3}$

Step 3.2.4

Rewrite the expression.

$\cot (θ) = 4 (\frac{- 1}{3})$

Step 3.3

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

$\cot (θ) = \frac{4 \cdot - 1}{3}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Multiply $4$ by $- 1$ .

$\cot (θ) = \frac{- 4}{3}$

Step 3.4.2

Move the negative in front of the fraction.

$\cot (θ) = - \frac{4}{3}$

Step 4

Approximate the result.

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