Find the Value Using the Unit Circle cot(315)

$\cot (315)$

Find the value using the definition of cotangent.

$\cot (315) = \frac{adjacent}{opposite}$

Substitute the values into the definition.

$\cot (315) = \frac{\frac{\sqrt{2}}{2}}{- \frac{\sqrt{2}}{2}}$

Simplify the result.

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{- 1}$

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

$- 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- 1$