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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