Find the Exact Value cos(14pi)

Problem

cos(14*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*n*π) for any integer n

2. Determine the number of full rotations in the given angle. Since 14*π=7×(2*π) the angle 14*π represents 7 full revolutions around the unit circle.

3. Simplify the angle to its coterminal equivalent within the interval [0,2*π)

14*π≡0*(mod()*2*π)

4. Evaluate the cosine of the simplified angle.

cos(14*π)=cos(0)

5. Recall the value of cos(0) from the unit circle, where the xcoordinate at 0 radians is 1

cos(0)=1

Final Answer

cos(14*π)=1

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