Trigonometry Examples

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

Step 1

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

Opposite : $- \frac{1}{\sqrt{2}}$

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

Step 2

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

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

Step 3

Simplify $\cot (θ)$ .

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Step 3.1

Cancel the common factor of $\frac{1}{\sqrt{2}}$ .

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Step 3.1.1

Cancel the common factor.

$\cot (θ) = \frac{\frac{1}{\sqrt{2}}}{- \frac{1}{\sqrt{2}}}$

Step 3.1.2

Rewrite the expression.

$\cot (θ) = \frac{1}{- 1}$

Step 3.1.3

Move the negative one from the denominator of $\frac{1}{- 1}$ .

$\cot (θ) = - 1 \cdot 1$

Step 3.2

Multiply $- 1$ by $1$ .

$\cot (θ) = - 1$