Equation f (t) = 7 + 5sin(0,5t - 1) ?

Question

The water depth variation is a function of the time t, which can be expressed with the equation f (t) = 7 + 5sin(0,5t - 1)

1) Find the deepest and lowest water depth, according to the equation.

2) Find f ’(t) and the speed the water depth changes, when the t=12

Answer 1

1)  in order to find deepest and lowest water level first  differentiate  the fn and set it to zero

find the values of t

sub in f "   if f"  >  0 it is     lowest  and <0 it is the deepest

other approach is sinA  can take values from -1 to 1

  

The water will be deepest when sinA  = 1

deepest      7+5    = 12

  

lowest            7  - 5  = 2

2)  f(t)  = 7+5sin(0.5t-1)

since f(t)  represents water level f 't represents speed at any time

f ' (t)  = 5 * 0.5 cos(0.5t - 1)  

f'(12)  = 5 * 0.5  cos(0.5 * 12  -1)   (take angle as radians)

         2.5 cos 5(radians)

        2.5 *  0.28366

    speed  0.709  units

  

Answer 2

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Hope it helps.