Find the Exact Value sec(-300 degrees )

Problem

sec(−300)

Solution

1. Use the even-odd property of the secant function, which states sec(−θ)=sec(θ)

sec(−300)=sec(300)

2. Find the coterminal angle or identify the quadrant. The angle 300 is in the fourth quadrant.

270<300<360

3. Determine the reference angle by subtracting the angle from 360

(θ_ref)=360−300=60

4. Apply the quadrant sign for secant. In the fourth quadrant, the cosine (and therefore secant) is positive.

sec(300)=sec(60)

5. Evaluate the secant using the reciprocal identity sec(θ)=1/cos(θ)

sec(60)=1/cos(60)

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

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

Final Answer

sec(−300)=2

Want more problems? Check here!