Question

find the maximum value of

Answer 1

\[\sin 2 \alpha+\sin 2 \beta+\sin 2\gamma \]
where \[\alpha,\beta,\gamma \ge 0,\text{and } \alpha+\beta+\gamma=180\]

Answer 2

sounds like a good candidate for a lagrange multiplier run ... maybe

Answer 3

and we say that a+b+g = pi to convert degrees to radians, not too sure if that matters tho

Answer 4

\[f(x,y,z)\sin 2x+\sin 2y+\sin 2z~:~g(x,y,z)=x+y+z-k\]
\[f_x2cos(2x)~:~\lambda g_x=\lambda~:~x=\frac12cos^{-1}\left(\frac{\lambda}{2}\right)\]
\[f_x2cos(2y)~:~\lambda g_y=\lambda\]
\[f_x2cos(2z)~:~\lambda g_z=\lambda\]
looks like x=y=z if ive done it correctly

Answer 5

\[\frac32cos^{-1}\left(\frac{\lambda}{2}\right)=\pi(or~180?)\]
\[\lambda=2cos\left(\frac23\pi(or~180?)\right)\]

Answer 6

\[\lambda=2cos\left(\frac23\pi\right)\]
\[\frac{\lambda}{2}=cos\left(\frac23\pi\right)\]
\[cos^{-1}\frac{\lambda}{2}=\frac23\pi\]
\[\frac12cos^{-1}\frac{\lambda}{2}=\frac\pi 3\]