Find the Exact Value sec((-7pi)/2)

Problem

sec(−(7*π)/2)

Solution

1. Find a coterminal angle by adding multiples of 2*π to the given angle until it falls within the interval [0,2*π)

θ=−(7*π)/2+2*π=−(7*π)/2+(4*π)/2=−(3*π)/2

θ=−(3*π)/2+2*π=−(3*π)/2+(4*π)/2=π/2

2. Apply the reciprocal identity for the secant function.

sec(π/2)=1/cos(π/2)

3. Evaluate the cosine of the coterminal angle using the unit circle.

cos(π/2)=0

4. Determine the value by substituting the cosine value back into the reciprocal expression.

sec(π/2)=1/0

5. Identify the result of division by zero.

1/0⇒Undefined

Final Answer

sec(−(7*π)/2)=Undefined

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