Question

sin(2x+x)=.5(sqrt(3)) solve

Answer 1

\(\large\color{black}{ \sin(2x+x)=\sin(2x)\cos(x)+\sin(x)\cos(2x)}\)
\(\large\color{black}{ \sin(2x+x)=2\sin(x)\cos(x)\cos(x)+\sin(x)(\cos^2x-\sin^2x)}\)
\(\large\color{black}{ \sin(2x+x)=2\sin(x)\cos^2(x)+\sin(x)(\cos^2x-\sin^2x)}\)
\(\large\color{black}{ \sin(2x+x)=2\sin(x)\cos^2(x)+\sin(x)\cos^2x-\sin^3x}\)
\(\large\color{black}{ \sin(2x+x)=3\sin(x)\cos^2(x)-\sin^3x}\)
\(\large\color{black}{ \sin(2x+x)=3\sin(x)(1-\sin^2x)-\sin^3x}\)
\(\large\color{black}{ \sin(2x+x)=3\sin(x)-3\sin^3x-\sin^3x}\)
\(\large\color{black}{ \sin(2x+x)=3\sin(x)-4\sin^3x}\)

I don't think they want you to do this, don't they? just approximate it?

Answer 2

it would be too hard to do all of this work....

Answer 3

i think we solve that equation
sin(3x) = 1/2 sqrt(3)

Answer 4

3x = arcsin( sqrt(3) / 2 )

3x = {pi/3 + 2pi * n , 4pi/3 + 2pi/n }

Answer 5

ohh, I haven't even thought that it is the same as sqrt{3}/2. have I seen sqrt{3}/2... lol