Find the Exact Value cos(-135 degrees )

Problem

cos(−135)

Solution

1. Apply the even-odd identity for the cosine function, which states that cos(−θ)=cos(θ)

cos(−135)=cos(135)

2. Find the reference angle for 135 by subtracting it from 180 because it is in the second quadrant.

(θ_ref)=180−135=45

3. Determine the sign of the cosine function in the second quadrant. Since cosine represents the x-coordinate on the unit circle, it is negative in the second quadrant.

cos(135)=−cos(45)

4. Substitute the known value for cos(45) which is √(,2)/2

cos(135)=−√(,2)/2

Final Answer

cos(−135)=−√(,2)/2

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