» Fill in the table x -2π -3π/4 -π -π/2 0 π/2 y » Plot the points on the graph π 3π/4 2π » Fill in the table x -2π -3π/4 -π -π/2 0 π/2 y » Plot the points on the graph π 3π/4 2π » One period = the intercepts, the maximum points, and the minimum points » Amplitude: of y = a sinx and y = a cosx represent half the distance between the maximum and minimum values of the function and is given by ˃ Amplitude = IaI » Period: Let be be a positive real number. The period of y = a sinbx and y = a cosbx is given by ˃ Period = (2π)/b » Sketch the graph y = 2sinx by hand on the interval [-π, 4π] » Sketch the graph of y = cos (x/2) by hand over the interval [-4π, 4π] » The constant c in the general equations ˃ y = a sin(bx – c) and y = a cos(bx – c) create horizontal translations of the basic sine and cosine curves. » One cycle of the period starts at bx – c = 0 and ends at bx – c = 2π » The number c/b is called a phase shift » Sketch the graph y = ½ sin (x – π/3) » Sketch the graph y = 2 + 3 cos2x » Find the amplitude, period, and phase shift for the sine function whose graph is shown. Then write the equation of the graph. » For a person at rest, the velocity v (in liters per second) of air flow during a respiratory cycle (the time from the beginning of one breath to the beginning of the next) is t given by v . 85 sin where t is the time (in seconds) . 3 (inhalation occurs when v> 0 and exhalation occurs when v < 0 ) a) Graph on the calculator b) Find the time for one full respiratory cycle c) Find the number of cycles per minute d) The model is for a person at rest. How might the model change for a person who is exercising? » A company that produces snowboards, which are seasonal products, forecast monthly sales t for 1 year to be S 74 .50 43 .75 cos 6 where S is the sales in thousands of units and t is the time in months, with t = 1 corresponding to January. a) Graph the function for a 1 year period b) What months have maximum sales and which months have minimum sales. » Throughout the day, the depth of the water at the end of a dock in Bangor, Washington varies with the tides. The table shows the depths (in feet) at various times during the morning. Time 12am Depth, y 3.1 2 am 4 am 6 am 8 am 10am 12pm 7.8 11.3 10.9 6.6 1.7 .9 » Use a trigonometric function to model this data. » A boat needs at least 10 feet of water to moor at the dock. During what times in the evening can it safely dock?