Warm Up Nov. 25th • 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

FunctionsGenerate 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…

Calculator investigation…

Y = sin x

Calculator investigation…

For cos 2x the waves occur MORE frequentlyFor cos ½x the wave occurs LESS frequently

For 3cosx the waves get steeper go from 3 to -3For ½cosx the waves get shorter b/w -1/2 to 1/2

For 2 + cos x the graph stays the same size moves up 2For -1 + cosx the graph stays the same size moves down 1

2

Amplitude

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

2

Period/Frequency

Length of the graph before it repeats. Where do I find this in the equation?

Max/Min

• Max/Min = • Max/Min =

• Max/Min = • 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

22

Sin (0) = 0. So Sine functions start at the origin.

The Cosine Curve

Y = cos x Y = -cos x

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