cosine: vertical question part 1 of 7 completed: 10 of 13 | my score: 8.48/13 pts (65.26%) save the graph to…

cosine: vertical question part 1 of 7 completed: 10 of 13 | my score: 8.48/13 pts (65.26%) save the graph to the right is a function of the form y = a sin (bx - c)+d, b>0. the five quarter - points of one cycle of the graph, from left to right, are given below. these five quarter - points on the graph correspond to the five quarter - points on the graph of y = sin x over the interval 0,2π. determine the equation of the specific function that is represented by the given graph based on the association of the labeled quarter - points and the quarter - points of the graph of y = sin x over the interval 0,2π. the quarter points are (π/4,2), (3π/8,7), (π/2,2), (5π/8, - 3), and (3π/4,2). a. the period of this function is (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

cosine: vertical question part 1 of 7 completed: 10 of 13 | my score: 8.48/13 pts (65.26%) save the graph to the right is a function of the form y = a sin (bx - c)+d, b>0. the five quarter - points of one cycle of the graph, from left to right, are given below. these five quarter - points on the graph correspond to the five quarter - points on the graph of y = sin x over the interval 0,2π. determine the equation of the specific function that is represented by the given graph based on the association of the labeled quarter - points and the quarter - points of the graph of y = sin x over the interval 0,2π. the quarter points are (π/4,2), (3π/8,7), (π/2,2), (5π/8, - 3), and (3π/4,2). a. the period of this function is (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Answer

Explanation:

Step1: Recall period - quarter - point relationship

The difference between the (x) - values of the first and the last quarter - points of one cycle gives the period of the function. Let (x_1=\frac{\pi}{4}) and (x_2 = \frac{3\pi}{4}).

Step2: Calculate the period

The period (T=x_2 - x_1). [T=\frac{3\pi}{4}-\frac{\pi}{4}=\frac{3\pi-\pi}{4}=\frac{2\pi}{4}=\frac{\pi}{2}]

Answer:

(\frac{\pi}{2})