Mathematics

Problem

Let

x=\sin t

and

y=\cos t

for

0<t<2\pi

. On which of the following intervals of

t

y

decreasing as

x

increases? a)

(0,\tfrac{\pi}{2})

(\pi,2\pi)

(0,\tfrac{\pi}{2})\cup(\pi,\tfrac{3\pi}{2})

(\tfrac{\pi}{2},\pi)\cup(\tfrac{3\pi}{2},2\pi)