In a precision manufacturing process, the vertical deflection vvv (in mm) of a control arm is governed by the input signal voltage uuu (in V), according to the function v=4πarcsin(u−2)v = \frac{4}{\pi} \arcsin(u - 2)v=π4arcsin(u−2). The graph of this function is plotted for its full natural domain, and it is strictly increasing between its two endpoints, LLL and MMM. Point MMM represents the state at which both the voltage and the deflection are at their maximum possible values.
State the coordinates of the endpoint MMM.
Select the correct answer from the options below:
(3,2)(3,π2)(2,0)(1,−2) (3, 2) \quad\quad (3, \frac{\pi}{2}) \quad\quad (2, 0) \quad\quad (1, -2) (3,2)(3,2π)(2,0)(1,−2)317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.