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

θ′=225−180=45

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

cos(225)=−cos(45)

4. Evaluate the exact value of the reference angle. The cosine of 45 is a known trigonometric value.

cos(45)=√(,2)/2

5. Combine the sign and the value to find the final result.

cos(225)=−√(,2)/2

Final Answer

cos(225)=−√(,2)/2

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