Find the Exact Value cos(135 degrees )

Problem

cos(135^∘)

Solution

1. Identify the angle 135^∘ on the unit circle and determine its quadrant. Since 90^∘<135^∘<180^∘ the angle is in Quadrant II.

2. Calculate the reference angle θ^′ by subtracting the angle from 180^∘

θ^′=180^∘−135^∘=45^∘

3. Determine the sign of the cosine function in Quadrant II. In this quadrant, xcoordinates are negative, so cos(135^∘) must be negative.

4. Apply the reference angle value. The cosine of 45^∘ is √(,2)/2

cos(135^∘)=−cos(45^∘)

5. Substitute the known value to find the exact result.

cos(135^∘)=−√(,2)/2

Final Answer

cos(135^∘)=−√(,2)/2

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