Finish Examples for 2 nd Block

Warm UpMay 13 th Sketch a graph of the following:

Homework Check/Questions?? #AmplitudePeriodVertical ShiftHorizontal Shift 12π/ ½2π2π0π /3π0-π/6 612π/3-3-π/6 71π30 81π0 912π2π π 1032π2π0 111π0π 1214π4π2π

Writing Equations of Sine & Cosine Graphs

Examples Write a sine function for the given requirements. 1.Amplitude of 4, Period of 2π 2.Amplitude of 3, Period of π 3.Amplitude of 5, Period of π/2 and Vertical Shift of -2 4.Amplitude of 1, Period of 2π/3 and Vertical Shift of 6

What is the amplitude?

What is the period?

Is it possible to write an equation with no horizontal shift?

What is the vertical shift?

What is an equation of the graph?

What is the equation of the graph?

What is an equation of the graph?

The equation below models the height (in feet) of the tide along a certain coastal area, as compared to average sea level. Assuming t = 0 is midnight, graph this function over a 12-hr period. a) What will the height of the tide be at 5 A.M.? b) Is the tide rising or falling at this time? c) When is the first time the tide is 4 feet below sea level?

The temperature in an office is controlled by an electronic thermostat. The temperatures vary according to the sinusoidal function: where y is the temperature (ºC) and x is the time in hours past midnight. a.) What is the temperature in the office at 9 A.M. when employees come to work? b.) What are the maximum and minimum temperatures in the office?

Tidal motion is periodic. If the height of the water in a harbor rose to a maximum height of 15 feet at 6:00pm, dropped to a minimum level of 3 feet by 3:00am and then rose back to a maximum of 15 feet at 12:00pm. Sketch a graph for the height of the water in terms of the number of hours after noon on the first day. (t = 0 is 6 pm) Write a function that represents the height, h, of the water, t hours after 6pm on the first day.

Tidal motion is periodic. If the height of the water in a harbor rose to a maximum height of 15 feet at 6:00pm, dropped to a minimum level of 3 feet by 3:00am and then rose back to a maximum of 15 feet at 12:00pm. What will the height of the water be at midnight on the first day? What is the first time that the height of the water will be 12 ft?

The water level varies from low tide to high tide. Low tide is 12 inches and occurs at 10 am. At high tide, which occurs at 4 pm, the water level rises 60 inches. Sketch a graph for the height of the water in terms of the number of hours after 10am on the first day. (t = 0 is 10am) Write a function that represents the height, h, of the water, t hours after 10am on the first day.

The water level varies from low tide to high tide. Low tide is 12 inches and occurs at 10 am. At high tide, which occurs at 4 pm, the water level rises 60 inches. What will the height of the water be at 8pm on the first day? What is the first time that the height of the water will be 48 inches?