# Math Help - need help finding how man solutions there are please.

1. ## need help finding how man solutions there are please.

how many solutions are there on the interval [0,2pi]?
cos(x)sin(x)+3cos(x)+sin(x)+3=0

Im looking at this problem and Im just lost.

2. Here is a hint

Note that it can be rewritten as

$\cos(x)\sin(x)+\sin(x)+3\cos(x)+3=0$

Now factor by grouping to get

$\sin(x)[\cos(x)+1]+3[\cos(x)+1]=(\cos(x)+1)(\sin(x)+3)=0$

Now use the zero factor principle to solve.