In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Solve, for 0<x⩽π0 < x \leqslant \pi0<x⩽π, the equation 6sinxtanx+11=cosx6 \sin x \tan x + 11 = \cos x6sinxtanx+11=cosx giving your answer in radians to 3 significant figures.
A hydrographic surveyor models the water depth in a shipping channel. The depth, HHH metres, ttt hours after midnight, is modelled by the equation H=8.5+4.2sin(kt+15)∘0⩽t<24H = 8.5 + 4.2 \sin(kt + 15)^\circ \quad 0 \leqslant t < 24H=8.5+4.2sin(kt+15)∘0⩽t<24 where kkk is a constant. Use the equation of the model to answer parts (a) to (c).
Given that
Find all possible values for kkk, giving each answer to 2 decimal places.
Given further that 10<k<2010 < k < 2010<k<20
Find the maximum water depth in the shipping channel,
Find the time of day at which this maximum depth occurs. Give your answer to the nearest minute.
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.