Trigonometry Examples

(2 \sqrt{5}, 4)

$(2 \sqrt{5}, 4)$

Step 1

To find the

\cot (θ)

$\cot (θ)$ between the x-axis and the line between the points

(0, 0)

$(0, 0)$ and

(2 \sqrt{5}, 4)

$(2 \sqrt{5}, 4)$ , draw the triangle between the three points

(0, 0)

$(0, 0)$ ,

(2 \sqrt{5}, 0)

$(2 \sqrt{5}, 0)$ , and

(2 \sqrt{5}, 4)

$(2 \sqrt{5}, 4)$ .

Opposite :

4

$4$

Adjacent :

2 \sqrt{5}

$2 \sqrt{5}$

Step 2

\cot (θ) = \frac{Adjacent}{Opposite}

$\cot (θ) = \frac{Adjacent}{Opposite}$ therefore

\cot (θ) = \frac{2 \sqrt{5}}{4}

$\cot (θ) = \frac{2 \sqrt{5}}{4}$ .

\frac{2 \sqrt{5}}{4}

$\frac{2 \sqrt{5}}{4}$

Step 3

Cancel the common factor of

2

$2$ and

4

$4$ .

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Step 3.1

Factor

2

$2$ out of

2 \sqrt{5}

$2 \sqrt{5}$ .

\cot (θ) = \frac{2 (\sqrt{5})}{4}

$\cot (θ) = \frac{2 (\sqrt{5})}{4}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

2

$2$ out of

4

$4$ .

\cot (θ) = \frac{2 \sqrt{5}}{2 \cdot 2}

$\cot (θ) = \frac{2 \sqrt{5}}{2 \cdot 2}$

Step 3.2.2

Cancel the common factor.

\cot (θ) = \frac{2 \sqrt{5}}{2 \cdot 2}

$\cot (θ) = \frac{2 \sqrt{5}}{2 \cdot 2}$

Step 3.2.3

Rewrite the expression.

\cot (θ) = \frac{\sqrt{5}}{2}

$\cot (θ) = \frac{\sqrt{5}}{2}$

\cot (θ) = \frac{\sqrt{5}}{2}

$\cot (θ) = \frac{\sqrt{5}}{2}$

\cot (θ) = \frac{\sqrt{5}}{2}

$\cot (θ) = \frac{\sqrt{5}}{2}$

Step 4

Approximate the result.

\cot (θ) = \frac{\sqrt{5}}{2} \approx 1.11803398

$\cot (θ) = \frac{\sqrt{5}}{2} \approx 1.11803398$

(2 \sqrt[]{5}, 4)

$(2 \sqrt[]{5}, 4)$

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