Solving for x: (sin x)^6 + (cos x)^6 = 5/6 ((sin x)^4 + (cos x)^4)

no name · Feb 28, 2005

hey ...

find (x) ...
(sin x )^6 + (cos x) ^6 = 5/6 ( (sin x)^4 + (cos x)^4)

cheers

Padford · Feb 28, 2005

x= 22.5
.. I think

dextercioby · Feb 28, 2005

There's the same problem posted in the "Brain Teasers" Section where I've given the correct answers...

Daniel.

HallsofIvy · Feb 28, 2005

Padford said:

x= 22.5
.. I think

If a problem involving trig functions does not specifically involve angle measured in degrees, x must be in "radians".

x= pi/8 is correct.

Pseudo Statistic · Feb 28, 2005

How do you solve such a problem? (Involving both functions)

dextercioby · Mar 1, 2005

Use that:\sin^{2}x=1-\cos^{2}x and the fact that the powers in the equation are even...

Daniel.

Zurtex · Mar 1, 2005

Erm, I think if you play around with it a bit you should be able to reduce it to :

\cos 4x = 0