Find the Exact Value sec(-240 degrees )

Problem

sec(−240)

Solution

1. Apply the even-odd identity for the secant function, which states sec(−θ)=sec(θ)

sec(−240)=sec(240)

2. Find the reference angle for 240 Since 240 is in the third quadrant, the reference angle is 240−180=60

(θ_ref)=60

3. Determine the sign of the secant function in the third quadrant. Since cos(θ) is negative in the third quadrant, sec(θ) is also negative.

sec(240)=−sec(60)

4. Evaluate the secant of the reference angle. Since cos(60)=1/2 its reciprocal is 2

sec(60)=2

5. Combine the value and the sign to find the final result.

sec(240)=−2

Final Answer

sec(−240)=−2

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