Evaluate cos(225 degrees )

Problem

cos(225^∘)

Solution

1. Identify the quadrant of the angle. Since 180^∘<225^∘<270^∘ the angle 225^∘ lies in the third quadrant.

2. Determine the sign of the cosine function. In the third quadrant, the cosine of an angle is negative.

3. Calculate the reference angle. The reference angle (θ_ref) is found by subtracting 180^∘ from the given angle.

(θ_ref)=225^∘−180^∘=45^∘

4. Apply the reference angle property. The value of cos(225^∘) is equal to −cos(45^∘)

cos(225^∘)=−cos(45^∘)

5. Substitute the known value for cos(45^∘)

cos(45^∘)=√(,2)/2

Final Answer

cos(225^∘)=−√(,2)/2

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