## cutiecomittee123 one year ago what is the minimum value of the function y=-1+6cos(2pi/7(x-5))

1. anonymous

just graph the function..

2. cutiecomittee123

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

3. anonymous

yes

4. 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

5. anonymous

not that $-1\le \cos(Z) \le1$

6. anonymous

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

7. anonymous

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

8. anonymous

the last line should be $-7 \le -1+6\cos(\frac{ 2 \pi }{ 7 }(x-5))\le5$

9. anonymous

something along those lines..

10. 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?