Find the Exact Value sec(330)

Problem

sec(330^∘)

Solution

1. Identify the reference angle by finding the difference between 330^∘ and 360^∘ because the angle is in the fourth quadrant.

(θ_ref)=360^∘−330^∘=30^∘

2. Determine the sign of the secant function in the fourth quadrant. Since sec(θ)=1/cos(θ) and cosine is positive in the fourth quadrant, the result will be positive.

sec(330^∘)=sec(30^∘)

3. Apply the reciprocal identity for secant.

sec(30^∘)=1/cos(30^∘)

4. Substitute the known exact value for cos(30^∘)=√(,3)/2

sec(330^∘)=1/√(,3)/2

5. Simplify the fraction by multiplying by the reciprocal.

sec(330^∘)=2/√(,3)

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

sec(330^∘)=(2√(,3))/3

Final Answer

sec(330^∘)=(2√(,3))/3

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