Find the Value Using the Unit Circle cos(225 degrees )

Problem

cos(225)

Solution

1. Identify the position of the angle 225 on the unit circle. Since 180<225<270 the angle lies in the third quadrant.

2. Determine the reference angle by subtracting 180 from the given angle.

(θ_ref)=225−180=45

3. Recall the cosine value for the reference angle 45 from the unit circle.

cos(45)=√(,2)/2

4. Apply the sign for the third quadrant. In the third quadrant, the xcoordinate (cosine) is negative.

cos(225)=−cos(45)

5. Substitute the known value to find the final result.

cos(225)=−√(,2)/2

Final Answer

cos(225)=−√(,2)/2

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