Find the Exact Value sec(-150 degrees )

Problem

sec(−150)

Solution

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

sec(−150)=sec(150)

2. Determine the reference angle for 150 Since 150 is in the second quadrant, the reference angle is 180−150=30

(θ_ref)=30

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(150)=−sec(30)

4. Evaluate the secant of the reference angle. Since cos(30)=√(,3)/2 the secant is the reciprocal.

sec(30)=2/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

2/√(,3)=(2√(,3))/3

6. Combine the results to find the final value.

sec(−150)=−(2√(,3))/3

Final Answer

sec(−150)=−(2√(,3))/3

Want more problems? Check here!