Find the Exact Value sec(300)

Problem

sec(300)

Solution

1. Identify the reference angle by finding the difference between 300 and the nearest x-axis angle, which is 360

360−300=60

2. Determine the quadrant of the angle. Since 300 is between 270 and 360 it lies in Quadrant IV.

3. Determine the sign of the secant function in Quadrant IV. Since sec(θ)=1/cos(θ) and cosine is positive in Quadrant IV, secant is also positive.

sec(300)=sec(60)

4. Apply the reciprocal identity for secant.

sec(60)=1/cos(60)

5. Substitute the known value cos(60)=1/2 into the expression.

1/(1/2)=2

Final Answer

sec(300)=2

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