Find the Exact Value sec(6)

Problem

sec(6)

Solution

1. Identify the input as an angle in radians. Since there is no degree symbol, 6 represents 6 radians.

2. Relate the secant function to the cosine function using the reciprocal identity.

sec(x)=1/cos(x)

3. Substitute the value 6 into the identity.

sec(6)=1/cos(6)

4. Determine if the value can be simplified further. Since 6 is not a standard multiple of π (like π/6 π/4 or π/3, the exact value is expressed in terms of the trigonometric function itself.

Final Answer

sec(6)=1/cos(6)

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