sine: vertical\nquestion\npart 1 of 7\ncompleted: 9 of 13 | my score: 7.63/13 pts (58.67%)\nsave\nthe graph…

sine: vertical\nquestion\npart 1 of 7\ncompleted: 9 of 13 | my score: 7.63/13 pts (58.67%)\nsave\nthe 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.\nthe quarter points are (π/4,0), (3π/4, - 5), (5π/4,0), (7π/4,5), and (9π/4,0).\n a. the period of this function is \nby step lify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)\nclear all\ncheck answer

sine: vertical\nquestion\npart 1 of 7\ncompleted: 9 of 13 | my score: 7.63/13 pts (58.67%)\nsave\nthe 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.\nthe quarter points are (π/4,0), (3π/4, - 5), (5π/4,0), (7π/4,5), and (9π/4,0).\n a. the period of this function is \nby step lify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)\nclear all\ncheck answer

Answer

Explanation:

Step1: Recall period - formula

For a sine - function $y = A\sin(Bx - C)+D$, the period $T$ is given by $T=\frac{2\pi}{B}$. Also, the distance between two consecutive quarter - points of a sine - function over one period is $\frac{T}{4}$.

Step2: Calculate the distance between two consecutive quarter - points

The $x$ - values of two consecutive quarter - points are $x_1=\frac{\pi}{4}$ and $x_2 = \frac{3\pi}{4}$. The distance between them is $\Delta x=\frac{3\pi}{4}-\frac{\pi}{4}=\frac{\pi}{2}$.

Step3: Find the period

Since the distance between two consecutive quarter - points is $\frac{T}{4}$, and $\frac{T}{4}=\frac{\pi}{2}$. Then, we can solve for $T$ by multiplying both sides of the equation by $4$. So, $T = 2\pi$.

Answer:

$2\pi$