Find the Exact Value cos(-pi/9)

Problem

cos(−π/9)

Solution

1. Apply the even-odd identity for the cosine function, which states that cos(−θ)=cos(θ)

2. Substitute the value θ=π/9 into the identity.

3. Identify that π/9 radians is equivalent to 20

4. Determine if a simpler radical form exists. Since 20 is not a standard reference angle (like 30 45 or 60, the exact value is typically left in trigonometric form unless using complex nested radicals.

Final Answer

cos(−π/9)=cos(π/9)

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