Is sin(10) Irrational? Proving the Irrationality of sin(10) in Degrees

[SrEstroncio]

Homework Statement

Prove $\sin{10}$, in degrees, is irrational.

Homework Equations

None, got the problem as is.

The Attempt at a Solution

Im kinda lost.

 

[STEMucator]

Homework Statement

Prove $\sin{10}$, in degrees, is irrational.

Homework Equations

None, got the problem as is.

The Attempt at a Solution

Im kinda lost.

Okay, are you familiar with proof by contradiction?

Start by contradicting the statement :

Suppose that sin(10) is irrational.

 

[Dick]

Homework Statement

Prove $\sin{10}$, in degrees, is irrational.

Homework Equations

None, got the problem as is.

The Attempt at a Solution

Im kinda lost.

Let x=sin(10). You'll want to find a polynomial x satisfies and show it has no rational root. Hint: sin(30)=1/2=sin(10+10+10).

 

[SrEstroncio]

I should suppose sin(10) is rational, if i am to contradict the statement, shouldn't i?

 

[jedishrfu]

yes and that means that sin(10) can be represented by the ratio of two integers a and b sin(10) = a/b

next step...

 

[Dick]

I should suppose sin(10) is rational, if i am to contradict the statement, shouldn't i?

Zondrina's hint contains nothing of any real substance to start solving the problem. Mine does. I suggest you start trying it.