Find the Exact Value sec(120 degrees )

Problem

sec(120)

Solution

1. Identify the reference angle for 120 by subtracting it from 180 because it is in the second quadrant.

180−120=60

2. Determine the sign of the secant function in the second quadrant. Since sec(θ)=1/cos(θ) and cosine is negative in the second quadrant, secant is also negative.

sec(120)=−sec(60)

3. Recall the reciprocal identity for secant.

sec(60)=1/cos(60)

4. Substitute the known exact value for cos(60)=1/2

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

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

sec(120)=−2

Final Answer

sec(120)=−2

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