Evaluate sec(30)

Problem

sec(30^∘)

Solution

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

sec(θ)=1/cos(θ)

2. Substitute the given angle of 30^∘ into the expression.

sec(30^∘)=1/cos(30^∘)

3. Recall the exact value of cos(30^∘) from the unit circle or a special right triangle (30^∘−60^∘−90^∘.

cos(30^∘)=√(,3)/2

4. Calculate the reciprocal of the cosine value.

sec(30^∘)=1/√(,3)/2

sec(30^∘)=2/√(,3)

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

sec(30^∘)=(2⋅√(,3))/(√(,3)⋅√(,3))

sec(30^∘)=(2√(,3))/3

Final Answer

sec(30^∘)=(2√(,3))/3

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