Find the Exact Value sec(585)

Problem

sec(585)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to bring it within the range of 0 to 360

585−360=225

2. Identify the quadrant for 225 Since 180<225<270 the angle lies in Quadrant III.

3. Determine the reference angle by subtracting 180 from the angle.

(θ_ref)=225−180=45

4. Determine the sign of the secant function in Quadrant III. Since cosine (and therefore secant) is negative in Quadrant III, the result will be negative.

sec(225)=−sec(45)

5. Evaluate the secant of the reference angle. Since cos(45)=√(,2)/2 the secant is the reciprocal.

sec(45)=2/√(,2)=√(,2)

6. Apply the sign to find the final value.

sec(585)=−√(,2)

Final Answer

sec(585)=−√(,2)

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