Find the Exact Value sec((3pi)/2)

Problem

sec((3*π)/2)

Solution

1. Identify the definition of the secant function in terms of the cosine function.

sec(θ)=1/cos(θ)

2. Determine the value of the cosine function at the given angle (3*π)/2 on the unit circle.

cos((3*π)/2)=0

3. Substitute the value of the cosine into the secant expression.

sec((3*π)/2)=1/0

4. Conclude that since division by zero is not defined, the value of the expression does not exist.

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Final Answer

sec((3*π)/2)=undefined

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