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).

For more information, refer to the link given below:

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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

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step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.