Find the Exact Value cos(-225 degrees )

Problem

cos(−225^∘)

Solution

1. Apply the even-odd identity for the cosine function, which states cos(−θ)=cos(θ)

cos(−225^∘)=cos(225^∘)

2. Find the reference angle by determining how far 225^∘ is from the nearest xaxis (180^∘.

Reference Angle=225^∘−180^∘=45^∘

3. Determine the quadrant of the angle. Since 225^∘ is between 180^∘ and 270^∘ it lies in Quadrant III.

4. Determine the sign of the cosine function in Quadrant III. Since cosine represents the xcoordinate on the unit circle, it is negative in Quadrant III.

cos(225^∘)=−cos(45^∘)

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

cos(225^∘)=−√(,2)/2

Final Answer

cos(−225^∘)=−√(,2)/2

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