Find the Exact Value cos(-(7pi)/3)

Problem

cos(−(7*π)/3)

Solution

1. Use the even-odd property of the cosine function, which states that cos(−θ)=cos(θ)

cos(−(7*π)/3)=cos((7*π)/3)

2. Find a coterminal angle within the standard interval [0,2*π] by subtracting 2*π from the argument.

(7*π)/3−2*π=(7*π)/3−(6*π)/3

(7*π)/3−(6*π)/3=π/3

3. Identify the exact value of the cosine function at the reference angle π/3 (or 60 using the unit circle or special triangles.

cos(π/3)=1/2

Final Answer

cos(−(7*π)/3)=1/2

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