cutiecomittee123
  • cutiecomittee123
what is the minimum value of the function y=-1+6cos(2pi/7(x-5))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
just graph the function..
cutiecomittee123
  • cutiecomittee123
I dont have my calculator and I dont want to graph it, is there any other way to calculate it?
anonymous
  • anonymous
yes

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More answers

baru
  • baru
the lowest value that 'cos' can take is -1. so the the lowest value the function can take is y=-1 + 6*(-1) =-7
anonymous
  • anonymous
not that \[-1\le \cos(Z) \le1 \]
anonymous
  • anonymous
so\[-1 \le \cos(\frac{ 2 \pi }{ 7 }(x-5))\le1\] \[-6 \le 6\cos(\frac{ 2 \pi }{ 7 }(x-5))\le6\] \[-7 \le -1+6\cos(\frac{ 2 \pi }{ 7 }(x-5))\le7\]
anonymous
  • anonymous
this tells us that our minimum value for this function is -7 and our max value os 5
anonymous
  • anonymous
the last line should be \[-7 \le -1+6\cos(\frac{ 2 \pi }{ 7 }(x-5))\le5\]
anonymous
  • anonymous
something along those lines..
ybarrap
  • ybarrap
$$ y=-1+6\cos(2\pi/7(x-5)) $$ Break it down The smallest that \(6\cos(2\pi/7(x-5))\) can be is -6. See that? -1 is a constant and the lowest it can be is -1. So, the lowest y will be is -1 + (-6) = -7. Does this make sense?

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