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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