# Thread: Find the value K

1. ## Find the value K

If $
siny = xsin(a+y)
$
and $
\frac{dy}{dx} = K \frac{sin^2y}{x^2}
$
, find K

2. Originally Posted by zorro
If $
siny = xsin(a+y)
$
and $
\frac{dy}{dx} = K \frac{sin^2y}{x^2}
$
, find K
I'm assuming that a is constant. If we expand your sine relationship and divide by x then $\frac{\sin y}{ x} = \sin a \cos y + \cos a \sin y$ then divide by $\sin y$ so

$\sin a \cot y + \cos a = \frac{1}{x}$ and upon differentiation gives $- \sin a \csc^2 y y' = - \frac{1}{x^2}$ which solving for y ' gives

$y' = \frac{1}{\sin a} \frac{\sin^2 y}{x^2}$

in which we can identify K.

3. ## Thanks mite....

Originally Posted by Danny
I'm assuming that a is constant. If we expand your sine relationship and divide by x then $\frac{\sin y}{ x} = \sin a \cos y + \cos a \sin y$ then divide by $\sin y$ so

$\sin a \cot y + \cos a = \frac{1}{x}$ and upon differentiation gives $- \sin a \csc^2 y y' = - \frac{1}{x^2}$ which solving for y ' gives

$y' = \frac{1}{\sin a} \frac{\sin^2 y}{x^2}$

in which we can identify K.

thanks mite
cheers