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.
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Here is a hint Note that it can be rewritten as $\displaystyle \cos(x)\sin(x)+\sin(x)+3\cos(x)+3=0$ Now factor by grouping to get $\displaystyle \sin(x)[\cos(x)+1]+3[\cos(x)+1]=(\cos(x)+1)(\sin(x)+3)=0$ Now use the zero factor principle to solve.