Find the Exact Value sec(-45)

Problem

sec(−45)

Solution

1. Apply the even-odd identity for the secant function, which states that sec(−θ)=sec(θ)

sec(−45)=sec(45)

2. Use the reciprocal identity to express secant in terms of cosine.

sec(45)=1/cos(45)

3. Substitute the known value for cos(45) which is √(,2)/2

sec(45)=1/√(,2)/2

4. Simplify the fraction by multiplying by the reciprocal.

sec(45)=2/√(,2)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,2)

sec(45)=(2√(,2))/2

6. Simplify the expression by canceling the common factor of 2.

sec(45)=√(,2)

Final Answer

sec(−45)=√(,2)

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