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 ˚

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

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

Calculator investigation…

Y = sin x

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

22 Amplitude Height of the graph. (either above or below the x-axis) Where do I find this in the equation?

22 Period/Frequency Length of the graph before it repeats. Where do I find this in the equation?

Max/Min

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

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)

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

Finding Properties in Equations General Form: Y = Asin(Bx) + D Y = Acos(Bx) + D

Finding Properties in Equations General Form: Y = Atan (Bx) + D

The Sine Curve Y = sin x Y = -sin x 22 22 Sin (0) = 0. So Sine functions start at the origin.

The Cosine Curve Y = cos xY = -cos x 22 22 Cos (0) = 1. So Cosine functions start at (0, 1).

The Tangent Curve

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

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

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

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

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

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

Homework Finish the 8 graphs