Find the Exact Value cos((7pi)/2)

Problem

cos((7*π)/2)

Solution

1. Identify the angle in terms of full rotations by dividing the coefficient of π by the denominator.

(7*π)/2=3.5*π

2. Determine the coterminal angle within the standard range [0,2*π) by subtracting multiples of 2*π

(7*π)/2−2*π=(7*π)/2−(4*π)/2

(7*π)/2−(4*π)/2=(3*π)/2

3. Evaluate the cosine function at the coterminal angle (3*π)/2 using the unit circle.

cos((3*π)/2)=0

Final Answer

cos((7*π)/2)=0

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