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+5=2cosx6 \sin x \tan x + 5 = 2 \cos x6sinxtanx+5=2cosx giving your answer in radians to 3 significant figures.
The dissolved oxygen concentration, DDD mg/L, in a fish pond ttt hours after midnight is modelled by the equation D=15+10sin(kt−35)∘0⩽t<24D = 15 + 10 \sin(kt - 35)^\circ \quad 0 \leqslant t < 24D=15+10sin(kt−35)∘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 0<k<150 < k < 150<k<15
Find the maximum dissolved oxygen concentration in the pond.
Find the time of day at which this maximum concentration 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.