Answer
$\cos y=\cos x-1$
The graph is given below.
Work Step by Step
Solve for $y$:
$y'=\frac{\sin x}{\sin y}$
$\frac{dy}{dx}=\frac{\sin x}{\sin y}$ (Separate the variables)
$\sin y dy=\sin x dx$ (Integrate)
$\int \sin y dy=\int \sin x dx$
$-\cos y=-\cos x-C$
$\cos y=\cos x+C$ (Substitute $y(0)=\pi/2$)
$\cos \frac{\pi}{2}=\cos 0+C$
$0=1+C$
$C=-1$
Thus, the solution is $\cos y=\cos x-1$ and here is the graph of the solution.
