Find the Exact Value cos(585)

Problem

cos(585)

Solution

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

585−360=225

2. Determine the quadrant of the angle 225 Since 180<225<270 the angle lies in Quadrant III.

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

(θ_ref)=225−180=45

4. Determine the sign of the cosine function in Quadrant III. In this quadrant, cosine values are negative.

cos(225)=−cos(45)

5. Substitute the known value for cos(45) which is √(,2)/2

cos(225)=−√(,2)/2

Final Answer

cos(585)=−√(,2)/2

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