tatianagomezb
  • tatianagomezb
How do I find the zeros of this function without graphing. f(x)=3+3 cos (x-π) I know the graph has lot of zeros. How would I find at least two and explain they repeat periodically? Thanks
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[f \left( x \right)=3+3\cos (x-\pi)=3+3\cos \left\{ -\left( \pi-x \right) \right\}=3+\cos \left( \pi-x \right)=3-3\cos x\] \[3-3\cos x=0,\cos x=1=\cos \left( 2n+1 \right)\frac{ \pi }{ 2 },x=\frac{ n \pi }{ 2 }\]
tatianagomezb
  • tatianagomezb
3+3cos{−(π−x)}=3+cos(π−x)=3−3cosx Good start, thanks but I don't understand why is this step valid. Why does the minus sign hace to change.
anonymous
  • anonymous
\[\cos \left( -x \right)=\cos x,\cos \left( \pi-x \right)=-\cos x\]

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tatianagomezb
  • tatianagomezb
Okay, I got it. Thanks again
anonymous
  • anonymous
yw

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