Find the Exact Value sec(240 degrees )

Problem

sec(240)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest xaxis. Since 240 is in the third quadrant, subtract 180 from the angle.

240−180=60

2. Determine the sign of the secant function in the third quadrant. In the third quadrant, only tangent and cotangent are positive, so secant is negative.

sec(240)=−sec(60)

3. Recall the definition of secant as the reciprocal of the cosine function.

sec(60)=1/cos(60)

4. Substitute the known value for cos(60) which is 1/2

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

5. Apply the negative sign determined in step 2 to find the final value.

sec(240)=−2

Final Answer

sec(240)=−2

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