Find the Exact Value sec(240)

Problem

sec(240)

Solution

1. Identify the reference angle by determining the quadrant in which 240 lies. Since 180<240<270 the angle is in Quadrant III.

2. Calculate the reference angle θ′ using the formula for Quadrant III: θ′=θ−180

θ′=240−180=60

3. Determine the sign of the secant function in Quadrant III. Since sec(θ)=1/cos(θ) and cosine is negative in Quadrant III, the result will be negative.

sec(240)=−sec(60)

4. Evaluate the exact value using the reciprocal identity sec(60)=1/cos(60)

cos(60)=1/2

sec(60)=1/(1/2)=2

5. Apply the negative sign determined in step 3 to find the final value.

sec(240)=−2

Final Answer

sec(240)=−2

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