Find the Exact Value sec(300)

Problem

sec(300^∘)

Solution

1. Identify the reference angle by finding the difference between 300^∘ and the nearest x-axis angle, which is 360^∘

360^∘−300^∘=60^∘

2. Determine the quadrant of the angle. Since 300^∘ is between 270^∘ and 360^∘ it lies in Quadrant IV.

3. Determine the sign of the secant function in Quadrant IV. Since sec(θ)=1/cos(θ) and cosine is positive in Quadrant IV, secant is also positive.

sec(300^∘)=sec(60^∘)

4. Apply the reciprocal identity for secant.

sec(60^∘)=1/cos(60^∘)

5. Substitute the known value cos(60^∘)=1/2 into the expression.

1/(1/2)=2

Final Answer

sec(300^∘)=2

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