Final answer:
The maximum value of the function y = -61 cos(72π (x-5)) is 61, found by considering that the maximum value of the cosine function is 1, and then negating the product of -61 and 1.
Step-by-step explanation:
The function given is y = -61 cos(72π (x-5)). To find the maximum value of this trigonometric function, we need to consider the properties of the cosine function. The cosine function oscillates between -1 and 1, so the maximum value of cos(θ) for any angle θ is 1. The maximum value of the function y will therefore be the product of -61 and the maximum value of the cosine function, which is -61 × 1. However, since there is a negative sign in front of the 61, the actual maximum value will be the negation of this product, resulting in 61.
Therefore, none of the options A. -\frac{1}{6} B. \frac{1}{6} C. \frac{1}{3} D. -\frac{1}{3} are correct because they do not match the correct maximum value. The correct maximum value of the function is 61.