Question

graph the function from x=0 and x=2 pie for y=8 cos^2x-4

Answer 1

Do you have to graph it by hand?

Answer 2

no i have a series of choices

Answer 3

Ok. So in this case you can narrow things down really quickly if you know about cos(x) over that same interval.

1. When is cos(x) = 0 ?
2. When is cos(x) = 1 ?

Answer 4

I'm sorry I'm still confused, what do you mean by 'when is cos(x)=o?'

Answer 5

What value of x makes cos(x) = 0 ?

Answer 6

isnt it cos 90?

Answer 7

Yes. cos(90) = 0 if we're in degree mode.
But this problem wants you to use radian mode. (everything in terms of pi).

So 90 degrees = ___ in radians?

Answer 8

I honestly have no idea.

Answer 9

Hm, ok. I'd recommend reviewing the basics -- sin, cos, tan, the unit circle, basically.
http://www.touchmathematics.org/topics/trigonometry (click the "sin" , "cos", "tan" , etc.) buttons under the circle to hide/show different graphs.

Answer 10

I know sin, cos, tan, and the unit circle. I just want to how you simply y=8cos^2x-4 if you understand what I am trying to say

Answer 11

I need to factor it but i cant figure that part out

Answer 12

There is no simplification needed. Given the graphs you should be able to see which it is by knowing how cos(x) alone behaves.

For instance, the greatest value cos(x) takes on is 1. That means the greatest value (cos(x))^2 takes on is also 1. But you're multiplying (cos(x))^2 by 8... so the greatest value it can take on is 8. BUT ... you're also subtracting 4 from it, so that means the greatest value it can take on is +4. That cuts out the graphs which have a max of y = 3.

Then you have to know what cos(0) = ...
If you know that, you should be able to figure out which of the remaining graphs represent your curve. :)