Question

Help me with this equation can you please help me

Answer 1

`h=asinbx+4`

In the function h, the value of a represents the amplitude of the trigonometric function, this amplitude represents half the distance between the maximum point and minimum point of the curve, according to the statement the innertube's height fluctuates between 2 meters and 6 meters, then,

`\begin{gathered} a=(max-min)/(2) \\ a=(6-2)/(2) \\ \\ a=(4)/(2) \\ a=2 \end{gathered}`

then, b can be found through the period of a trigonometric function, the period can be understood as the time or interval in which the function starts at a maximum and gets back to the same point, in the statement the interval is equal to 10, by definition of a trigonometric function can be found by:

`p=(2\pi)/(b)`

clear the equation for b,

`b=(2\pi)/(p)`

since the period is equal to 10,

`\begin{gathered} b=(2\pi)/(10) \\ \\ b=(\pi)/(5) \end{gathered}`

the complete function should be,

`h=2sin((\pi)/(5))+4`

Answer:

`a=2;b=(\pi)/(5)`