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)^\circ L=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.
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.