- #1

- 26

- 0

I've started to work on the it, just tell me if I'm on the right track.

cos (45-30) = ([tex]\sqrt{3}[/tex] + 1) / 2[tex]\sqrt{2}[/tex] so cos 15 is irrational.

cos3x = 4cos^3x - 3cos x [tex]\Rightarrow[/tex] cos 5 is irrational

cos 4x....... cos 20

If this is a bad way, maybe someone knows a better one.

Here is what I think a better way:

cos3x = 4cos^3x - 3cosx so cos20 is the solution for 8x^3 - 6x - 1 and this one has no rational solutions so cos20 is irrational

cos (45-30) = ([tex]\sqrt{3}[/tex] + 1) / 2[tex]\sqrt{2}[/tex] so cos 15 is irrational.

cos3x = 4cos^3x - 3cos x [tex]\Rightarrow[/tex] cos 5 is irrational

cos 4x....... cos 20

If this is a bad way, maybe someone knows a better one.

Here is what I think a better way:

cos3x = 4cos^3x - 3cosx so cos20 is the solution for 8x^3 - 6x - 1 and this one has no rational solutions so cos20 is irrational

Last edited: