 Describe the transformations that change y = cosx into…  y = cos (x-30)  y = 3cosx  y = -cosx.

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Presentation transcript:

 Describe the transformations that change y = cosx into…  y = cos (x-30)  y = 3cosx  y = -cosx

Aims: To become familiar with the sine, cosine and tangent functions.

 Name: To know the sine, cosine and tangent functions.  Describe: The where the sine, cosine and tangent functions come from and sketch their graphs.  Apply transformations to these functions and start to use a graphical calculator to draw them.

 P225 Ex 1A Q2,3 + Revision of C2/C1  Next Lesson: More Trig Graphs and Functions  Hipparchus – Greek Mathematician (Born in Modern Day Turkey) Discovered the basis of trigonometry c140BC but is more famous for his works in astronomy.

 Visual Demonstrations of sine and cosine from the unit circle.  hp?id=33 hp?id=33

 The same transformation rules we have seen so far can be applied to these graphs. You must be aware of how these graphs influence key elements/ properties.  E.g.

 Using the transparencies match the functions to the graphs.

 Ampiltude:  Max/Min:  Period (Stretches):  Osscilates About:

Amplitude = 1 Period = 120° Oscillates about 0

Amplitude = 2 Period = 90° Oscillates about 0

Amplitude = 4 Period = 1080° Oscillates about 0

Amplitude = 4 Period = 180° Oscillates about -3

Amplitude = 2 Period = 6° Oscillates about 5

Amplitude = 10 Period = 100° Oscillates about 12

 y=sinx  y=cosx

 Transformations, Trig Graphs and Radians Task  Mathematician:  c500CE this Indian Mathematician that first considered the trigonometric ratios sine and cosine as functions.

 How do you identify the maximum and minimum values of trigonometric functions involving sine and cosine...  E.g. What are the maximum and minimum values of 4+2sinx?

 Given sinx=0.23 and 0≤x≤360 what are the possible values of x?  Use calc to get principle value…

 Given sinx=0.23 and 0≤x≤360 what are the possible values of x?  Use graph to find further values…

 Graph Mode – All Powerful!