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)274 exam-style questions on Edexcel A Level Maths Trigonometric Functions, covering 6.1 Secant, Cosecant and Cotangent, 6.2 Graphs of Sec x, Cosec x and Cot x, 6.3 Using Sec x, Cosec x and Cot x, 6.4 Trigonometric Identities, and 6.5 Inverse Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.