Find the Exact Value cos((5pi)/4)

Problem

cos((5*π)/4)

Solution

1. Identify the quadrant of the angle (5*π)/4 Since π<(5*π)/4<(3*π)/2 the angle lies in Quadrant III.

2. Determine the sign of the cosine function in Quadrant III. In this quadrant, the xcoordinates are negative, so cos(θ) is negative.

3. Calculate the reference angle θ′ For an angle in Quadrant III, the reference angle is found using θ′=θ−π

θ′=(5*π)/4−π=π/4

4. Evaluate the cosine of the reference angle. The exact value for cos(π/4) is √(,2)/2

5. Apply the sign from step 2 to the value from step 4 to find the final result.

cos((5*π)/4)=−cos(π/4)

Final Answer

cos((5*π)/4)=−√(,2)/2

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