Find the Exact Value cos(5pi)

Problem

cos(5*π)

Solution

1. Identify the periodicity 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. Reduce the angle by subtracting multiples of 2*π to find a coterminal angle within the interval [0,2*π)

3. Calculate the coterminal angle by subtracting 4*π from 5*π

5*π−4*π=π

4. Evaluate the cosine of the resulting angle π using the unit circle. At π radians (180 degrees), the coordinates on the unit circle are (−1,0)

5. Determine the value of cos(π) which corresponds to the x-coordinate.

cos(π)=−1

Final Answer

cos(5*π)=−1

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