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=119
Given 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.
Practise Edexcel A Level Maths 7.5 Proving Trigonometric Identities with exam-style questions for A Level Maths. 27 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.