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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