Find the Exact Value sec(-30 degrees )

Problem

sec(−30)

Solution

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

sec(−30)=sec(30)

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

sec(30)=1/cos(30)

3. Substitute the known value for cos(30) which is √(,3)/2

1/cos(30)=1/√(,3)/2

4. Simplify the fraction by multiplying by the reciprocal of the denominator.

1/√(,3)/2=2/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

Final Answer

sec(−30)=(2√(,3))/3

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