Find the Exact Value cos(10pi)

Problem

cos(10*π)

Solution

1. Identify the period of the cosine function. The cosine function has a period of 2*π meaning cos(θ)=cos(θ+2*π*k) for any integer k

2. Determine the number of full rotations. Since 10*π is an even multiple of π we can write it as 5×2*π

3. Simplify the angle using the periodicity. Because 10*π represents 5 full rotations around the unit circle, the terminal side of the angle is the same as the angle 0

4. Evaluate the cosine at the simplified angle. The value of cos(0) is 1

Final Answer

cos(10*π)=1

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