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

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

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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.

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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.

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Visual Demonstrations of sine and cosine from the unit circle. http://integralmaths.org/course/view.p hp?id=33 http://integralmaths.org/course/view.p hp?id=33

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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.

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Using the transparencies match the functions to the graphs.

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

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Amplitude = 1 Period = 120° Oscillates about 0

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Amplitude = 2 Period = 90° Oscillates about 0

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Amplitude = 4 Period = 1080° Oscillates about 0

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Amplitude = 4 Period = 180° Oscillates about -3

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Amplitude = 2 Period = 6° Oscillates about 5

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Amplitude = 10 Period = 100° Oscillates about 12

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y=sinx y=cosx

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

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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?

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

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

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Graph Mode – All Powerful!

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Warm UpNov. 25 th Determine whether to us the Law of Sine or Cosine and solve for the missing pieces. 1. Δ ABC with a = 12, B = 13 ˚, C= 24 ˚ 2. Δ ABC.

Warm UpNov. 25 th Determine whether to us the Law of Sine or Cosine and solve for the missing pieces. 1. Δ ABC with a = 12, B = 13 ˚, C= 24 ˚ 2. Δ ABC.

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