The efficiency E E\,E of a precision-engineered joint in a robotic limb is determined by the tilt angle ϕ \phi\,ϕ such that
(sinϕ+12cosϕ)2+(4sinϕ−3cosϕ)2=119 (\sin \phi + 12 \cos \phi)^2 + (4 \sin \phi - 3 \cos \phi)^2 = 119 (sinϕ+12cosϕ)2+(4sinϕ−3cosϕ)2=119Given that the joint is positioned at an obtuse angle, such that π2<ϕ<π\displaystyle \frac{\pi}{2} < \phi < \pi2π<ϕ<π, determine the exact value of sinϕ\sin \phisinϕ. Fully justify your answer.
