Warm UpNov. 25 th Determine whether to us the Law of Sine or Cosine and solve for the missing...

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Warm Up Nov. 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 with a = 12, b = 26, C = 50˚

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Transcript of Warm UpNov. 25 th Determine whether to us the Law of Sine or Cosine and solve for the missing...

  • Slide 1
  • Warm UpNov. 25 th Determine whether to us the Law of Sine or Cosine and solve for the missing pieces. 1. ABC with a = 12, B = 13 , C= 24 2. ABC with a = 12, b = 26, C = 50
  • Slide 2
  • Graphing Sine & Cosine & Tangent Functions Generate graphs of the sine, cosine, and tangent functions.
  • Slide 3
  • Graphing Trigonometric Functions Vocabulary Identify Vocabulary on Graphs Identify Vocabulary in equations Graphing Trig Functions Match Trig Functions with Graph
  • Slide 4
  • Calculator investigation
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  • Y = sin x
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  • Calculator investigation For cos 2x the waves occur MORE frequently For cos x the wave occurs LESS frequently For 3cosx the waves get steeper go from 3 to -3 For cosx the waves get shorter b/w -1/2 to 1/2 For 2 + cos x the graph stays the same size moves up 2 For -1 + cosx the graph stays the same size moves down 1
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  • 22 Amplitude Height of the graph. (either above or below the x-axis) Where do I find this in the equation?
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  • 22 Period/Frequency Length of the graph before it repeats. Where do I find this in the equation?
  • Slide 9
  • Max/Min
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  • End Behavior All basic trig functions (sin, cos, tan) are continuous This leaves us with no end behavior
  • Slide 11
  • Y-Intercepts In general form, we find the y-intercept by plugging 0 in for x. Sin(0) = 0 Cos(0) = 1 Tan(0) = 0 This tells us what ordered pair contains the y- intercept. Sine = (0, 0), Cosine = (0, 1), Tangent = (0, 0)
  • Slide 12
  • Identify the following: Amplitude, period, max/min, y- intercept
  • Slide 13
  • Finding Properties in Equations General Form: Y = Asin(Bx) + D Y = Acos(Bx) + D
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  • Finding Properties in Equations General Form: Y = Atan (Bx) + D
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  • The Sine Curve Y = sin x Y = -sin x 22 22 Sin (0) = 0. So Sine functions start at the origin.
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  • The Cosine Curve Y = cos xY = -cos x 22 22 Cos (0) = 1. So Cosine functions start at (0, 1).
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  • The Tangent Curve
  • Slide 18
  • Degrees to Radians In the past we have used degrees to represent angles, we can also use radians
  • Slide 19
  • The Basic curve Y = sin x Y = -sin x Y = cos x Y = -cos x
  • Slide 20
  • Graph the Function (on sheet from yesterday) y = 3Sin(1/2x) y = Sin(2x)
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  • Graph the Function y = 3Cos(1/2x) y = Cos(2x)
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  • Graph the Function y = Tan(1/2x) y = Tan(2x)
  • Slide 23
  • Graph the Function y = 2 sin(x) +1 y = 3cos(x) - 1
  • Slide 24
  • Homework Finish the 8 graphs