Find the Exact Value sec(-300 degrees )

Problem

sec(−300^∘)

Solution

1. Use the even-odd property of the secant function, which states sec(−θ)=sec(θ)

sec(−300^∘)=sec(300^∘)

2. Find the coterminal angle or identify the quadrant. The angle 300^∘ is in the fourth quadrant.

270^∘<300^∘<360^∘

3. Determine the reference angle by subtracting the angle from 360^∘

(θ_ref)=360^∘−300^∘=60^∘

4. Apply the quadrant sign for secant. In the fourth quadrant, the cosine (and therefore secant) is positive.

sec(300^∘)=sec(60^∘)

5. Evaluate the secant using the reciprocal identity sec(θ)=1/cos(θ)

sec(60^∘)=1/cos(60^∘)

6. Substitute the known value for cos(60^∘)=1/2

sec(60^∘)=1/(1/2)=2

Final Answer

sec(−300^∘)=2

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