# need help finding how man solutions there are please.

• June 26th 2010, 12:46 PM
ninobrn99
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.
• June 26th 2010, 01:28 PM
TheEmptySet
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.