how many solutions in the inteval 0

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how many solutions in the inteval 0

Mathematics
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Hey, start by applying your `Zero Factor Property`,\[\large\rm 2x \sin3x-1=0\qquad\qquad\qquad \cos2x+1=0\]
Are you sure that first one has an \(\large\rm x\) and \(\large\rm sin3x\) in it? :o Hmm that's going to be tricky..
Yes

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The second one shouldn't be too bad. Subtract 1 from each side,\[\large\rm \cos(\color{orangered}{2x})=-1\]Recall that cosine is -1 at an angle of pi.\[\large\rm \color{orangered}{2x=\pi+2k \pi}\]Any number of full spins will get us back to that same point, so we add an amount of 2pi's on the end like that. Solving for x,\[\large\rm x=\frac{\pi}{2}+k \pi\]For k=0, we get \(\large\rm x=\frac{\pi}{2}\) For k=1, we get \(\large\rm x=\frac{3\pi}{2}\) Any other values of k will take us outside of our interval. So that's all the solutions we're getting from the second bracket.
Hopefully that makes sense. Hmm I'm not sure what to do about the other bracket though :p
Oh, it simply says "how many", not to actually find them... oh oh interesting.
Is this for calculus? :)
cause maybe we could count the critical points.
hmm
Thanks for your help and Yes it is for calculus. :)
Let's see if any of these smart guys have an idea :d @ganeshie8 @Kainui @dan815

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