Question

what is the minimum value of the function y=-1+6cos(2pi/7(x-5))

Answer 1

just graph the function..

Answer 2

I dont have my calculator and I dont want to graph it, is there any other way to calculate it?

Answer 3

yes

Answer 4

the lowest value that 'cos' can take is -1. so the the lowest value the function can take is y=-1 + 6*(-1)
=-7

Answer 5

not that \[-1\le \cos(Z) \le1 \]

Answer 6

so\[-1 \le \cos(\frac{ 2 \pi }{ 7 }(x-5))\le1\]
\[-6 \le 6\cos(\frac{ 2 \pi }{ 7 }(x-5))\le6\]
\[-7 \le -1+6\cos(\frac{ 2 \pi }{ 7 }(x-5))\le7\]

Answer 7

this tells us that our minimum value for this function is -7 and our max value os 5

Answer 8

the last line should be

\[-7 \le -1+6\cos(\frac{ 2 \pi }{ 7 }(x-5))\le5\]

Answer 9

something along those lines..

Answer 10

$$
y=-1+6\cos(2\pi/7(x-5))
$$
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?