Find the Exact Value cos(135)

Problem

cos(135)

Solution

1. Identify the angle's position on the unit circle. The angle 135 is located in the second quadrant.

2. Determine the reference angle. For an angle θ in the second quadrant, the reference angle θ′ is calculated as 180−θ

3. Calculate the reference angle: 180−135=45

4. Apply the cosine sign for the second quadrant. In the second quadrant, the xcoordinate is negative, so cos(135) must be negative.

5. Evaluate the cosine of the reference angle. The exact value of cos(45) is √(,2)/2

6. Combine the sign and the value to find the result.

Final Answer

cos(135)=−√(,2)/2

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