# Math Help - Find the equation of the curve given that...

1. ## Find the equation of the curve given that...

Can anyone solve the question in this attachement, try to show working where possible so i can see what you have done.

question attached

2. Originally Posted by duckegg
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:

$\frac{dy}{dt} = 3sint$

when t=25 degrees , y = 2. Find the equation of the curve.

Separate variables:

$1 dy = 3 sint dt$

Integrate both sides:
$y = -3 cost + C$

Plug in t=25 y=2 (Just remember that t is in degrees when you evaluate in your graphing calculator, and not in radians)
$2 = -3cos 25 + C$

Solve for C:
$C = 2 + 3cos25$

So the curve has equation $y = -3cost(t) + 3 cos(25) + 2$

To check, differentiate and evaluate.

Good luck!