# For mathematicians

if sin(x)+cos(x)=1/3 then Sin(x)^5+Cos(x)^5=?

## Answers and Replies

Staff Emeritus
What do you think it is? We do not do your homework for you here. Show some work, please.

One more thing: Please post homework problems in one of the homework forums.

Homework Helper
x5+ y5= (x+ y)(x4- x3y+ x2y2+ xy3+ y4)

Staff Emeritus
x5+ y5= (x+ y)(x4- x3y+ x2y2+ xy3+ y4)

You have a sign error, Halls.
5+ y5= (x+ y)(x4- x3y+ x2y2- xy3+ y4)

Homework Helper
Let u=sin(x) v=cos(x). We know u+v, and since (u+v)^2=1+2uv, we know uv, hence we know a basis of the symmetric functions in u,v, and we can, if we are bothered work out, u^5+v^5. That I feel is far less interesting than the knowledge about symmetric function theory...

But the OP seems to be posting all these questions as challenges, rather than questions for which he seeks the answer.

mhill
sin(x)+cos(x)=1/3 then 1+2sin(x)cos(x)=1/9= 1+sin(2x)

so sin(2x)=-8/9 then 2x=arcsin(-8/9) once you have got 'x' the rest is easy