Question

Write the formula of the function, where xxx is entered in radians.f(x)=

Answer 1

`f(x)\text{ = 3cos \lparen}(\pi)/(5)x)\text{ + 5}`

Step-by-step explanation:

Here, we want to write the formula of the function

The general form is:

`f(x)\text{ = Acos\lparen B\lparen x-c\rparen\rparen + D}`

A is the amplitude

D is the mid-value

We have the amplitude as:

`(max-min)/(2)\text{ = }(8-2)/(2)\text{ = }(6)/(2)\text{ =3}`

Now, let us get the period value:

The period is the distance from max to max or from min to min

From the question, we have that as 10

The value of D is the mid-value which is the sum of the y-values divided by 2 (8+2/2 = 5)

Now,let us get the value of B

`B\text{ = }\frac{2\pi}{Period\text{ }}\text{ = }(2\pi)/(10)\text{ = }(\pi)/(5)`

Thus, we have the equation as:

`f(x)\text{ = 3 cos\lparen}(\pi)/(5)x)\text{ + 5}`