Find the Exact Value cos((20pi)/9)

Problem

cos((20*π)/9)

Solution

1. Identify the period of the cosine function, which is 2*π

2. Find the coterminal angle within the interval [0,2*π) by subtracting 2*π from the given angle.

3. Calculate the subtraction:

(20*π)/9−2*π=(20*π)/9−(18*π)/9

4. Simplify the result to find the equivalent angle:

(20*π)/9−(18*π)/9=(2*π)/9

5. Determine if the value can be simplified further. Since (2*π)/9 (or 40 is not a standard reference angle, the exact value is expressed in terms of the simplified angle.

Final Answer

cos((20*π)/9)=cos((2*π)/9)

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