Simplify cos(3pi)

Problem

cos(3*π)

Solution

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

2. Subtract the period from the angle to find a coterminal angle within the standard interval [0,2*π)

cos(3*π)=cos(3*π−2*π)

cos(3*π)=cos(π)

3. Evaluate the cosine of the resulting angle using the unit circle. At the angle π (or 180, the coordinates on the unit circle are (−1,0) Since cos(θ) corresponds to the x-coordinate:

cos(π)=−1

Final Answer

cos(3*π)=−1

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