Question

Identify the maximum and minimum values of the function y = 3 cos x in the interval [-2π, 2π].

Answer 1

Well, y=3cos(x) is a periodic function, so we can just think of it on [0,2Pi].

We know that the maximum value of cos(x) on [0,2Pi] is 1, and that the minimum value is -1. So the maximum value of 3cos(x) must be 3, and the minimum must be at -3.

If you also need the x values that correspond to the y values, you just need to solve 1=cos(x) and -1=cos(x)

Answer 2

How would I solve those last 2 equations?

Answer 3

I would look at the unit circle: http://www.mathsisfun.com/geometry/images/circle-unit-304560.gif

Answer 4

Okay. But how would I solve them?

Answer 5

Actually, here is a better one: http://www.sciencedigest.org/UnitCircle.gif

The numbers of inside the parenthesis are the values of cos(x) and sin(x) at various values between 0 and 2Pi.

So for example, at Pi/3 you see that cos(x)=1/2

Just look for places where cos(x)=1 or -1, and then look at the radians (or the degrees, both are valid).

Answer 6

Okay, thanks.

Answer 7

None of them have cos(x)=1 or -1

Answer 8

NVM.

Answer 9

Sorry.

Answer 10

So the max and min are 1 and -1?

Answer 11

No, the max and min are 3 and -3. The max and min values of cos(x) are 1 and -1, but you're multiplying those each by 3.

Answer 12

Oh, okay.

Answer 13

Thanks for the Unit Circle, I needed a new one. :P

Answer 14

You're welcome.