Find the Exact Value cos(-(9pi)/2)

Problem

cos(−(9*π)/2)

Solution

1. Identify the angle and use the even-odd property of the cosine function, which states cos(−θ)=cos(θ)

cos(−(9*π)/2)=cos((9*π)/2)

2. Find a coterminal angle by subtracting multiples of 2*π (or (4*π)/2 until the angle is within the interval [0,2*π)

(9*π)/2−2*π=(9*π)/2−(4*π)/2=(5*π)/2

(5*π)/2−2*π=(5*π)/2−(4*π)/2=π/2

3. Evaluate the cosine of the coterminal angle π/2 using the unit circle.

cos(π/2)=0

Final Answer

cos(−(9*π)/2)=0

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