Trigonometry Examples

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

Step 1

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

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Factor $- 1$ out of $\frac{- \sqrt{2}}{2}$ .

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

Step 3.2

Rewrite $- \frac{\sqrt{2}}{2}$ as $- 1 \frac{\sqrt{2}}{2}$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Divide $- 1$ by $1$ .

$\cot (θ) = - 1$