8 3. On a particular day, the depth of water in a river estuary at a specific location is modelled by the equation sin cos 0 7 (I) x x D x π       = + +           2 3 6 3 3 where the depth of water is D metres at time x hours after midnight on that day. (a) Write down the depth of water at midnight, according to the model. (1) Using the substitution t x =       tan 6 (b) show that equation (I) can be re-written as D t t t = + + + 3 4 9 1 2 2 (3) (c) Hence determine, according to the model, the time after midnight when the depth of water is 5 metres for the first time. Give your answer to the nearest minute. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________