Question

A sinusoidal function with an amplitude of 13, a maximum value of 26, and a period of (2)/(3) is based on the parent function −cos(x). Which of the following represents the equation of this sinusoidal function?

Answer 1

The sine function oscillates between +1 and -1 every 2 radians. For the given conditions, a sinusoidal function based on −cos(x) with an amplitude of 13, maximum value of 26, and period of 2/3 is y = −13cos(3πx) + 13.

Step-by-step explanation:

The question requires us to find the equation of a sinusoidal function given the amplitude, maximum value, and period, and based on the parent function −cos(x). With an amplitude of 13 and a maximum value of 26, we can determine the vertical shift is +13. The period of the sinusoidal function is given as ⅓, and since the period of the cosine function is 2π, we can use this ratio to find the horizontal stretch factor, which turns out to be 3π. The equation of the sinusoidal function based on −cos(x) that meets the given conditions is therefore:

y = −13cos(3πx) + 13