If dy/dx= sin x/ cos y and y(0) = 3pi/2, find an equation for y in terms of x

dy / dx = sin x / cos y
 We rewrite the equation:
 (cos (y) * dy) = (sin (x) * dx)
 We integrate both sides of the equation:
 sin (y) = - cos (x) + C
 We use the initial condition to find the constant C:
 sin (3pi / 2) = - cos (0) + C
 -1 = -1 + C
 C = -1 + 1
 C = 0
 The equation is then:
 sin (y) = - cos (x)
 Clearing y:
 y = Arcosine (-cos (x))
 
 An equation for and in terms of x is:
 y = Arcosine (-cos (x))