Simplify cos((3pi)/4)

Problem

cos((3*π)/4)

Solution

1. Identify the angle (3*π)/4 on the unit circle. This angle is in the second quadrant because π/2<(3*π)/4<π

2. Determine the reference angle by subtracting the angle from π

Reference Angle=π−(3*π)/4

Reference Angle=π/4

3. Apply the cosine value for the reference angle π/4

cos(π/4)=√(,2)/2

4. Assign the correct sign based on the quadrant. In the second quadrant, the cosine function is negative.

cos((3*π)/4)=−√(,2)/2

Final Answer

cos((3*π)/4)=−√(,2)/2

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