Evaluate cos((7pi)/4)

Problem

cos((7*π)/4)

Solution

1. Identify the angle (7*π)/4 on the unit circle. This angle is in the fourth quadrant because (3*π)/2<(7*π)/4<2*π

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

Reference Angle=2*π−(7*π)/4

Reference Angle=π/4

3. Apply the cosine property for the fourth quadrant. In the fourth quadrant, the cosine of an angle is positive.

cos((7*π)/4)=cos(π/4)

4. Evaluate the cosine of the reference angle using known trigonometric values.

cos(π/4)=√(,2)/2

Final Answer

cos((7*π)/4)=√(,2)/2

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