Can anyone solve the question in this attachement, try to show working where possible so i can see what you have done.
question attached
The question is:
$\displaystyle \frac{dy}{dt} = 3sint$
when t=25 degrees , y = 2. Find the equation of the curve.
Separate variables:
$\displaystyle 1 dy = 3 sint dt$
Integrate both sides:
$\displaystyle y = -3 cost + C$
Plug in t=25 y=2 (Just remember that t is in degrees when you evaluate in your graphing calculator, and not in radians)
$\displaystyle 2 = -3cos 25 + C$
Solve for C:
$\displaystyle C = 2 + 3cos25$
So the curve has equation $\displaystyle y = -3cost(t) + 3 cos(25) + 2$
To check, differentiate and evaluate.
Good luck!