Question

Let a be a rational number with 0 13 years ago

Answer 1

\[\cos(3 \pi a)+2\cos(2 \pi a)=0\]
(Anlge measurents are in radiens )
Prove that \[a=2/3\]

Answer 2

did u try writing cos(3pi*a) using the formula of cos 3x ? and cos(2pi*a) using cos 2x and getting a cubic equation ?

Answer 3

x=pi*a

Answer 4

\[4x^3-4x^2-3x+2=0\]

Answer 5

\[(2x-1)(2x^2-x-2)=0\]
\[x=1/2\]
\[\cos(3\pi a)=1/2\]

Answer 6

\[3\pi a=\pm \pi/3+2\pi k\]

Answer 7

i made mistake \[4x^3+4x^3-3x-2=0\]
\[(2x+1)(2x^2+x-2)=0\]
\[x=-1/2\]
\[\cos(\pi a)=\pm (\frac{ 2\pi }{ 3 })+2\pi k\]

Answer 8

last step\[\cos (\pi a)=-1/2\]
\[\pi a=\frac{ 2 \pi }{ 3 }\]

Answer 9

yipee

Answer 10

\[a=2/3\]

Answer 11

is that correct

Answer 12

??

Answer 13

guys can you say something

Answer 14

sorry i was afk, its correct

Answer 15

thanks