Find the Exact Value cos((-3pi)/4)

Problem

cos(−(3*π)/4)

Solution

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

cos(−(3*π)/4)=cos((3*π)/4)

2. Identify the reference angle for (3*π)/4 Since the angle is in the second quadrant, the reference angle is π−(3*π)/4=π/4

(θ_ref)=π/4

3. Determine the sign of the cosine function in the second quadrant. In Quadrant II, the xcoordinate is negative, so cos(θ) is negative.

cos((3*π)/4)=−cos(π/4)

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

−cos(π/4)=−√(,2)/2

Final Answer

cos(−(3*π)/4)=−√(,2)/2

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