Question

ANSWER NEEDED

On a windmill, the tip of one blade moves in a circular motion. The maximum height is 18 feet and the minimum height is 4 feet. The height of the tip of the blade (in feet) can be modeled by the function h(x)=−14sinx+18 where x is time in seconds. Use the inverse function to determine how many seconds it will take to make a full rotation for one blade.

Answer 1

`2\pi\ seconds=6.28\ seconds`

Explanation:

Trigonometric Functions

The trigonometric functions have a cyclic behavior, which means they perform a full cycle and then do it all again in their whole domain. If we know that

sinx=0

we can use the inverse sine function to know the values of x. In this case, all angles whose sine is 0.

X=0 is the trivial solution, but given the repetitive nature of the sine, we know the next cycle will repeat the same value. Each cycle occurs every
`2\pi` units of x, so the solution is

`x=0+2k\pi`

being k any integer number, positive or negative

The height of the tip of the blade (in feet) of our windmill has a motion described by the equation

`h(x)=-14sinx+18`

Let's start one cycle by setting x=0, so the initial value of h is

`h(0)=-14(0)+18=18`

The very next cycle will be when h=18 again

`-14sinx+18=18`

Or

sinx=0

Which next solution is

`x=2\pi`

So, it will take to make a full rotation for one blade a time of

`2\pi\ seconds=6.28\ seconds`