Find the Exact Value cos((9pi)/4)

Problem

cos((9*π)/4)

Solution

1. Identify the angle and determine if it is within the standard interval [0,2*π] Since (9*π)/4>2*π we need to find a coterminal angle.

2. Subtract 2*π from the angle to find the coterminal angle within the first rotation.

(9*π)/4−2*π=(9*π)/4−(8*π)/4

(9*π)/4−(8*π)/4=π/4

3. Evaluate the cosine of the coterminal angle. The value of cos(π/4) is a standard value from the unit circle.

cos(π/4)=√(,2)/2

Final Answer

cos((9*π)/4)=√(,2)/2

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