The graph of a sinusoidal function has a maximum point at (0,8) and then has a minimum point at (5,2). Write the formula of the function, where x is entered in radians.

The formula of the function, where x is entered in radians is 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:

where A is the amplitude.

Step 2 - Now, the value of A is given below:

A = 3

Step 3 - The value of C is calculated as:

C = 5

Step 4 - The time period is calculated as:

T = 10

Step 5 - So, the value of y is maximum at (x = 0).

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y = 3 cos(π/5 x) + 5

Step-by-step explanation:

The amplitude is half the difference of the min and max.

A = (8 − 2) / 2

A = 3

The midline is the average of the min and max.

C = (8 + 2) / 2

C = 5

The difference in the x values of the min and max is half the period.

T/2 = 5 − 0

T = 10

The function is a maximum at x = 0, so use cosine.

y = 3 cos(2π/10 x) + 5

y = 3 cos(π/5 x) + 5

answer: 45