Does cos^4 x = 0.25 + (cos 2x)/2 + (cos 4x + 1)/8?

[Chewy0087]

Homework Statement

express cos^4 x in terms of cos 4x and cos 2x given that

cos^ x = 0.5(1 + cos 2x)

The Attempt at a Solution

i did some playing around for a minute and came to this;

cos^4 x = 0.25 + (cos2x)/2 + (cos 4x +1)/8

and thought, great! now i'll just check it on wolfram however i got this;

http://www.wolframalpha.com/input/?i=y+=0.25+++(cos2x)/2+++(cos+4x++1)/8

as opposed to

http://www.wolframalpha.com/input/?i=cos+^4+x

now, just looking at the graphs it seems okay however none of the alternate forms or expansions are the same, i would love it if someone could just verify that I'm right it's quite an important question!

thanks again

 

[nietzsche]

your answer is correct

if you group everything over a common denominator it might become more apparent

 

[Chewy0087]

thanks a lot for that, it was really bugging me :D

 

[VietDao29]

thanks a lot for that, it was really bugging me :D

You can always try to graph as a way to check your work:

$$y = \cos ^ 4 x - \left( 0.25 + \frac{\cos (2x)}{2} + \frac{\cos(4x) + 1}{8} \right)$$

to see if it turns out to be the x axis. If it does, then, everything should be fine. :)

Btw, your expression can be further simplified to:

$$\cos ^ 4 x = {\color{red}\frac{5}{8}} + \frac{\cos (2x)}{2} + \frac{\cos(4x)}{8}$$

 

[nietzsche]

$$\cos ^ 4 x = {\color{red}\frac{5}{8}} + \frac{\cos (2x)}{2} + \frac{\cos(4x)}{8}$$

I got
$$\cos ^ 4 x = {\color{red}\frac{3}{8}} + \frac{\cos (2x)}{2} + \frac{\cos(4x)}{8}$$

 

[Chewy0087]

that's a good idea actually, thanks

i'm sure he meant 3/8