Find the Exact Value sec(-120 degrees )

Problem

sec(−120)

Solution

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

sec(−120)=sec(120)

2. Determine the reference angle for 120 Since 120 is in the second quadrant, the reference angle is 180−120=60

(θ_ref)=60

3. Identify 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)

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

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

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

sec(120)=−2

Final Answer

sec(−120)=−2

Want more problems? Check here!