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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 with a = 12, b = 26, C = 50 ˚

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Graphing Sine & Cosine & Tangent Functions Generate graphs of the sine, cosine, and tangent functions.

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Graphing Trigonometric Functions Vocabulary Identify Vocabulary on Graphs Identify Vocabulary in equations Graphing Trig Functions Match Trig Functions with Graph

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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 ½x the wave occurs LESS frequently For 3cosx the waves get steeper go from 3 to -3 For ½cosx 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?

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Max/Min

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End Behavior All basic trig functions (sin, cos, tan) are continuous This leaves us with no end behavior

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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)

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Identify the following: Amplitude, period, max/min, y- intercept

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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

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Degrees to Radians In the past we have used degrees to represent angles, we can also use radians

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The Basic curve Y = sin x Y = -sin x Y = cos x Y = -cos x

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Graph the Function (on sheet from yesterday) y = 3Sin(1/2x) y = ½ Sin(2x)

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Graph the Function y = 3Cos(1/2x) y = ½ Cos(2x)

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Graph the Function y = Tan(1/2x) y = Tan(2x)

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Graph the Function y = 2 sin(x) +1 y = 3cos(x) - 1

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Homework Finish the 8 graphs

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