Find the Exact Value sec(-225 degrees )

Problem

sec(−225)

Solution

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

sec(−225)=sec(225)

2. Find the reference angle for 225 Since 225 is in the third quadrant, the reference angle is 225−180=45

(θ_ref)=45

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

sec(225)=−sec(45)

4. Evaluate the secant of the reference angle. We know that cos(45)=√(,2)/2 so its reciprocal is sec(45)=√(,2)

sec(45)=√(,2)

5. Combine the sign and the value to find the final result.

sec(225)=−√(,2)

Final Answer

sec(−225)=−√(,2)

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