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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