Simplify cos(225)

Problem

cos(225^∘)

Solution

1. Identify the angle's position on the unit circle. The angle 225^∘ is in the third quadrant because 180^∘<225^∘<270^∘

2. Determine the reference angle. For an angle in the third quadrant, the reference angle is calculated as (θ_ref)=θ−180^∘

(θ_ref)=225^∘−180^∘=45^∘

3. Apply the sign for the quadrant. In the third quadrant, the cosine function is negative.

cos(225^∘)=−cos(45^∘)

4. Substitute the known value for the cosine of the reference angle.

cos(45^∘)=√(,2)/2

Final Answer

cos(225^∘)=−√(,2)/2

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