Question

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

Answer 1

Answer:

$f(x)\text{ = 3cos \lparen}\frac{\pi}{5}x)\text{ + 5}$

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:

$\frac{max-min}{2}\text{ = }\frac{8-2}{2}\text{ = }\frac{6}{2}\text{ =3}$

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

$B\text{ = }\frac{2\pi}{Period\text{ }}\text{ = }\frac{2\pi}{10}\text{ = }\frac{\pi}{5}$

Thus, we have the equation as:

$f(x)\text{ = 3 cos\lparen}\frac{\pi}{5}x)\text{ + 5}$