Evaluate cos(5pi)

Problem

cos(5*π)

Solution

1. Identify the period of the cosine function. The function cos(θ) 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 the coterminal angle within the interval [0,2*π)

5*π−2*(2*π)=5*π−4*π

5*π−4*π=π

3. Evaluate the cosine of the resulting angle. On the unit circle, the coordinates at π radians are (−1,0) Since cos(θ) corresponds to the x-coordinate:

cos(π)=−1

Final Answer

cos(5*π)=−1

Want more problems? Check here!