Download presentation

Presentation is loading. Please wait.

Published byDillon Cartlidge Modified over 2 years ago

1
*Sketch sine and cosine graphs *Use amplitude and period *Sketch translations of sine and cosine graphs

2
» One period = the intercepts, the maximum points, and the minimum points

3
» 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 = I a I » Period: Let be be a positive real number. The period of y = a sinbx and y = a cosbx is given by ˃Period = (2π)/b

4
» Sketch the graph y = 2sinx by hand on the interval [-π, 4π]

5
» Sketch the graph of y = cos (x/2) by hand over the interval [-4π, 4π]

6
» 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

7
» Sketch the graph y = ½ sin (x – π/3)

8
» Sketch the graph y = 2 + 3 cos2x

9
» Find the amplitude, period, and phase shift for the sine function whose graph is shown. Then write the equation of the graph.

10
» 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 given by where t is the time (in seconds). (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?

11
» A company that produces snowboards, which are seasonal products, forecast monthly sales for 1 year to be 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.

12
» 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. » 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? Time12am2 am4 am6 am8 am10am12pm Depth, y3.17.811.310.96.61.7.9

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google