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

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

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Solution Steps

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.

Final Answer: \(\csc(\theta)\) is approximately 1.414.

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