Find the Exact Value sec(-300)

Problem

sec(−300)

Solution

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

sec(−300)=sec(300)

2. Find the reference angle for 300 Since 300 is in the fourth quadrant, the reference angle is 360−300=60

(θ_ref)=60

3. Determine the sign of the secant function in the fourth quadrant. Since cos(θ) is positive in the fourth quadrant, sec(θ) is also positive.

sec(300)=sec(60)

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

sec(60)=1/cos(60)

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

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

6. Simplify the fraction.

sec(60)=2

Final Answer

sec(−300)=2

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