The formula of the function, where x is entered in radians is [tex]\rm y = 3 sin(\dfrac{\pi}{5}x) + 5[/tex] and this can be determined by using the given data.
Given :
The graph of a sinusoidal function has a maximum point at (0,8) and then has a minimum point at (5,2).
The following steps can be used in order to determine the formula of the function, where x is entered in radians:
Step 1 - The generalized sinusoidal function is given below:
[tex]\rm y = A sin(bx) + C[/tex]
where A is the amplitude.
Step 2 - Now, the value of A is given below:
[tex]\rm A = \dfrac{8-2}{2}[/tex]
A = 3
Step 3 - The value of C is calculated as:
[tex]\rm C = \dfrac{8+2}{2}[/tex]
C = 5
Step 4 - The time period is calculated as:
[tex]\rm \dfrac{T}{2}=5-0[/tex]
T = 10
Step 5 - So, the value of y is maximum at (x = 0).
[tex]\rm y = 3 sin(\dfrac{2\pi}{10}x) + 5[/tex]
[tex]\rm y = 3 sin(\dfrac{\pi}{5}x) + 5[/tex]
For more information, refer to the link given below:
https://brainly.com/question/6848432
