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.
137 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.