Identify the maximum and minimum values of the function y = 8 cos x in the interval [-2π, 2π].

Question

whpalmer4 · Answer

what is the range of $\cos x$ over that interval?

anonymous · Answer

I have no entire clue. I don't understand this at all.

whpalmer4 · Answer

What's the largest value that $\cos x$ ever has?

anonymous · Answer

8?

whpalmer4 · Answer

I asked about $\cos x$, not $8\cos x$

anonymous · Answer

I dont know

whpalmer4 · Answer

here's a hint:

anonymous · Answer

1

whpalmer4 · Answer

right. and the minimum value?

anonymous · Answer

-1. so for 8 cos x, the max would be 8 & the min would be -8?

whpalmer4 · Answer

you got it!

anonymous · Answer

so what does it mean by "in the interval [-2pi, 2pi]?

whpalmer4 · Answer

well, in this case, it doesn't really affect the answer.  if the interval had been something smaller, where you didn't have an entire cycle of $\cos x$, the answer might have been different.  For example, if the interval was $[0,\pi/4]$ then you would have to find the maximum and minimum values of $\cos x$ between those two points.  The max would still be 1, the min would be $\sqrt{2}/2$, and the answer to the question would be 8 and $4\sqrt{2}$ for max and min respectively.

anonymous · Answer

Okay, thanks so much!

marissalovescats · Answer

Because the amplitude is 8, then the height of each wave will be 8. So your max would be 8 and your min would be -8. I just had this question in my online class but with the number 10.