Find the Exact Value sec(300 degrees )

Problem

sec(300)

Solution

1. Identify the reference angle by finding the distance from the given angle to the nearest part of the xaxis. Since 300 is in the fourth quadrant, subtract it from 360

(θ_ref)=360−300=60

2. Determine the sign of the secant function in the fourth quadrant. Since sec(θ)=1/cos(θ) and cosine is positive in the fourth quadrant, the result will be positive.

sec(300)=sec(60)

3. Apply the reciprocal identity to relate the secant function to the cosine function.

sec(60)=1/cos(60)

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

sec(300)=1/(1/2)

5. Simplify the fraction by multiplying by the reciprocal.

sec(300)=2

Final Answer

sec(300)=2

Want more problems? Check here!