Sin^5(x)+Cos^5(x) Equation Solution for Mathematicians

  • Thread starter hadi amiri 4
  • Start date
In summary, to find the value of Sin(x)^5+Cos(x)^5, we can use the given equation and knowledge of symmetric function theory to solve for x and then plug it into the expression (sin(x)+cos(x))(sin(x)^4- sin(x)^3cos(x)+ sin(x)^2cos(x)^2+ sin(x)cos(x)^3+ cos(x)^4).
  • #1
hadi amiri 4
98
1
if sin(x)+cos(x)=1/3 then Sin(x)^5+Cos(x)^5=?
 
Mathematics news on Phys.org
  • #2
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.
 
  • #3
x5+ y5= (x+ y)(x4- x3y+ x2y2+ xy3+ y4)
 
  • #4
HallsofIvy said:
x5+ y5= (x+ y)(x4- x3y+ x2y2+ xy3+ y4)

You have a sign error, Halls.
5+ y5= (x+ y)(x4- x3y+ x2y2- xy3+ y4)
 
  • #5
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.
 
  • #6
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
 

1. What is the general solution for the equation Sin^5(x)+Cos^5(x)?

The general solution for this equation is not a simple algebraic expression, but rather a series of infinite solutions. One possible solution is x = pi/2 + 2kpi, where k is any integer.

2. Can this equation be solved using basic trigonometric identities?

Yes, this equation can be solved using the identities Sin(x)^2 + Cos(x)^2 = 1 and Sin(x)*Cos(x) = Sin(2x)/2.

3. Is there a specific method for solving this equation?

There is not a specific method for solving this equation, as it requires a combination of algebraic manipulation and application of trigonometric identities.

4. Are there any restrictions on the values of x for this equation?

There are no restrictions on the values of x for this equation, as the solutions are valid for all real numbers.

5. Can this equation be graphed?

Yes, this equation can be graphed by plugging in different values for x and plotting the resulting points. The graph will show a periodic pattern with a period of 2pi.

Similar threads

  • General Math
Replies
5
Views
308
Replies
2
Views
1K
  • General Math
Replies
3
Views
826
  • General Math
Replies
1
Views
157
  • General Math
Replies
3
Views
2K
  • General Math
Replies
11
Views
1K
  • General Math
Replies
1
Views
3K
Replies
2
Views
1K
  • General Math
Replies
1
Views
7K
Replies
3
Views
1K
Back
Top