4. Create an equation for a sine function that has a maximum value of 3, a minimum value of -5, and a period of % (3 marks) 5. The following graph represents a sine function in the form y = a sin b(x + ) + d or a cosine function in the form y = a cos b(x + ) +d . If @ = 0, and there is a minimum phase shift, write an equation of the graph in both forms. (5 marks) y 12 6. State the following, in radians, for the function y = tan(x), where xER. (3 marks) a) domain: b) range: c) period: d) x-intercept(s): e) y-intercept(s): f) equations of vertical asymptotes: 7. a) Consider the graphs of y = cos(2x) and y = - - over the domain - I S x S It. Solve for x using a graphical method. Use exact values. (3 marks) HINT: You may want to graph in degree mode and then convert your answers to radians. -4-4-4-4- _-0.5 b) State the general solution. (1 mark)8. On a particular day in the harbour, the equation of the sinusoidal function that represents the relationship between the depth of water, y, in metres, and the time, , in hours after midnight, is y = asin2(t + 2)) + 15. a) Calculate the depth of water 4 hours after midnight. (1 mark) b) State the maximum and minimum depths of water in the harbour. (1 mark) c) Calculate, as an exact value and a decimal to the nearest tenth of a metre, the depth of water at midnight. (2 marks) d) A large supertanker is in the harbour at midnight. It can remain in the harbour if the depth of water in the harbour is at least 12 metres. Since the minimum depth of water in the harbour is less than 12 metres, the tanker will need to leave the harbour before the depth falls below 12 metres. Explain clearly how to use a graphical approach to determine the latest time, to the nearest hour, that the supertanker can remain in the harbour. State an appropriate graphing calculator window. (3 marks) e) Calculate the latest time, to the whole hour, that the supertanker can remain in the harbour. (1 mark)