cosine: vertical question part 1 of 7 completed: 11 of 13 my score: 9.2/13 pts (70.76%) save the graph to…

cosine: vertical question part 1 of 7 completed: 11 of 13 my score: 9.2/13 pts (70.76%) save the graph to the right is a function of the form y = a cos (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 = cos 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 = cos x over the interval 0,2π. the quarter - points are (-π/2,-5),(-π/4,-2),(0,1),(π/4,-2), and (π/2,-5). 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: 11 of 13 my score: 9.2/13 pts (70.76%) save the graph to the right is a function of the form y = a cos (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 = cos 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 = cos x over the interval 0,2π. the quarter - points are (-π/2,-5),(-π/4,-2),(0,1),(π/4,-2), and (π/2,-5). 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 - finding formula

For the function $y = A\cos(Bx - C)+D$, the period $T$ is given by $T=\frac{2\pi}{B}$. We can also find the period using the $x$ - values of the quarter - points. The difference between the $x$ - values of two consecutive quarter - points of a cosine function over one period is $\frac{T}{4}$.

Step2: Identify two relevant quarter - points

Let's take two non - consecutive quarter - points with $x$ values $x_1=-\frac{\pi}{2}$ and $x_2=\frac{\pi}{2}$. The difference between these two $x$ values is $\Delta x=\frac{\pi}{2}-\left(-\frac{\pi}{2}\right)$.

Step3: Calculate the period

Since the difference between two non - consecutive quarter - points separated by 4 quarter - points (a full period) is related to the period, and $\frac{\pi}{2}-\left(-\frac{\pi}{2}\right)=\pi$, and this represents half of the period of the cosine function. So the period $T = \pi$.

Answer:

$\pi$