Find the Exact Value cos(225)

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 reference angle. The reference angle θ′ for an angle in the third quadrant is calculated as θ′=θ−180

3. Calculate the reference angle value.

θ′=225−180=45

4. Apply the sign rule for the cosine function. In the third quadrant, the cosine of an angle is negative.

cos(225)=−cos(45)

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

cos(225)=−√(,2)/2

Final Answer

cos(225)=−√(,2)/2

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