Simplify sec(225)

Problem

sec(225)

Solution

1. Identify the reference angle by determining the quadrant of 225 Since 180<225<270 the angle is in the third quadrant.

2. Calculate the reference angle (θ_r*e*ƒ) using the formula for the third quadrant.

(θ_r*e*ƒ)=225−180=45

3. Determine the sign of the secant function in the third quadrant. Since sec(θ)=1/cos(θ) and cosine is negative in the third quadrant, secant is also negative.

sec(225)=−sec(45)

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