Find the Exact Value sec(30)

Problem

sec(30)

Solution

1. Identify the relationship between the secant function and the cosine function using the reciprocal identity.

sec(θ)=1/cos(θ)

2. Substitute the given angle of 30 into the identity.

sec(30)=1/cos(30)

3. Determine the exact value of cos(30) using the unit circle or a special right triangle (30−60−90.

cos(30)=√(,3)/2

4. Calculate the reciprocal by dividing 1 by the value of the cosine.

sec(30)=1/√(,3)/2

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

sec(30)=2/√(,3)

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

sec(30)=(2√(,3))/3

Final Answer

sec(30)=(2√(,3))/3

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