Find the Exact Value cos(15pi)

Problem

cos(15*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*k*π) for any integer k

2. Reduce the angle by subtracting multiples of 2*π Since 15*π is an odd multiple of π we can write it as 14*π+π

3. Apply the periodicity rule. Since 14*π is 7×2*π the value of cos(15*π) is equivalent to cos(π)

4. Evaluate the cosine of the resulting angle. On the unit circle, the coordinates at π radians (180 are (−1,0)

5. Determine the x-coordinate, which represents the cosine value.

Final Answer

cos(15*π)=−1

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