The lateral displacement, LLL micrometres, of a high-precision industrial cutting head from its central axis is modelled by the equation
L=Asin(t−15)∘L = A \sin(t - 15)^\circL=Asin(t−15)∘
where AAA is a constant and ttt is the time in milliseconds since the start of a cycle.
A sensor detects that the first minimum displacement occurs at the point P(105,−12)P(105, -12)P(105,−12).
State the value of AAA.
The point QQQ is a maximum displacement point on the graph. Given that QQQ is the third maximum point recorded after point PPP, determine the coordinates of QQQ.
Practise Edexcel A Level Maths Trigonometry and Modelling with exam-style questions for A Level Maths. 100 questions 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, 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.