Simplify cos((7pi)/4)

Problem

cos((7*π)/4)

Solution

1. Identify the angle (7*π)/4 on the unit circle.

2. Determine the reference angle by subtracting the angle from 2*π since it is in the fourth quadrant.

Reference Angle=2*π−(7*π)/4

Reference Angle=π/4

3. Determine the sign of the cosine function in the fourth quadrant. In the fourth quadrant, the xcoordinate is positive, so cos(θ)>0

4. Evaluate the cosine of the reference angle.

cos(π/4)=√(,2)/2

5. Combine the value and the sign to find the final result.

cos((7*π)/4)=√(,2)/2

Final Answer

cos((7*π)/4)=√(,2)/2

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