Find the Exact Value sec(120)

Problem

sec(120)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest x-axis. Since 120 is in the second quadrant, the reference angle is 180−120=60

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

3. Recall the exact value of cos(60)

cos(60)=1/2

4. Apply the reciprocal identity to find the secant of the reference angle.

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

5. Combine the value with the appropriate sign for the second quadrant.

sec(120)=−2

Final Answer

sec(120)=−2

Want more problems? Check here!