Questions: Find the exact function value. csc(pi/4)

Transcript text: Find the exact function value. \[ \csc \frac{\pi}{4} \]

Solution

Step 1: Understand the Function

Recognize that $\csc(\theta) = \frac{1}{\sin(\theta)}$ .

Step 2: Find the Sine Value

For $\theta = 0.785$ , the $\sin(\theta)$ value is directly known or derived from special triangles.

Step 3: Calculate the Reciprocal

$\csc(\theta) = \frac{1}{\sin(\theta)} = \frac{1}{0.707}$ .

Step 4: Simplify the Expression

After rounding, $\csc(\theta)$ is approximately 1.414.

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