Find the exact value of the expression.

Ask by Robbins Curry. in the United States

Jan 24,2025

Question

Find the exact value of the expression. $$ \cot \left(\frac{\pi}{4}\right)=\square $$

UpStudy AI · Accepted Answer

To find the exact value of $$ \cot\left(\frac{\pi}{4}\right) $$, let's break it down step by step.

1. **Understanding Cotangent:**
   The cotangent function is defined as the ratio of the cosine to the sine of the same angle:
   $$
   \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}
   $$

2. **Evaluate $$ \cos\left(\frac{\pi}{4}\right) $$ and $$ \sin\left(\frac{\pi}{4}\right) $$:**
   For $$ \theta = \frac{\pi}{4} $$, which is 45 degrees:
   $$
   \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}
   $$
   $$
   \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}
   $$

3. **Calculate Cotangent:**
   Plugging these values into the cotangent formula:
   $$
   \cot\left(\frac{\pi}{4}\right) = \frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1
   $$

**Final Answer:**
$$
\cot\left(\frac{\pi}{4}\right) = 1
$$
$$ \cot\left(\frac{\pi}{4}\right) = 1 $$

Find the exact value of the expression.

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