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Graphs of other Trig Functions Section 4.6
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Graphs of other Trig Functions. Section 4.6. What is the cosecant x? Where is cosecant not defined? Any place that the Sin x = 0 The curve will not pass through these points on the x-axis. x = 0, π , 2 π. Cosecant Curve. Drawing the cosecant curve Draw the reciprocal curve - PowerPoint PPT Presentation

Transcript of Graphs of other Trig Functions

Graphs of other Trig Functions

Graphs of other Trig FunctionsSection 4.6Cosecant CurveWhat is the cosecant x?

Where is cosecant not defined?Any place that the Sin x = 0

The curve will not pass through these points on the x-axis.

x = 0, , 2 Cosecant CurveDrawing the cosecant curve

Draw the reciprocal curveAdd vertical asymptotes wherever curve goes through horizontal axisHills become Valleys and Valleys become HillsCosecant Curvey = Csc x y = Sin x-11

Cosecant Curvey = 3 Csc (4x ) y = 3 Sin (4x )a = 3b = 4Per. =

dis. =

c = P.S. =

-33

Cosecant Curvey = -2 Csc 4x + 2 y = -2 Sin 4x + 224

Secant CurveWhat is the secant x?

Where is secant not defined?Any place that the Cos x = 0

The curve will not pass through these points on the x-axis.

Secant Curvey = Sec 2x y = Cos 2x-11

Secant Curvey = Sec x y = Cos x-11

Graph these curvesy = 3 Csc (x 2)

y = 2 Sec (x + )

y = Csc (x - )

y = -2 Sec (4x + 2)

y = 3Csc (x 2) y = 3 Sin ( x 2)-33

y = 2Sec (x + ) y = 2 Cos (x + )-22

y = Csc (x - ) y = Csc (x - )-

y = -2 Sec (4 x + 2 ) -2 Cos (4 x + 2 )-22

Graph of Tangent and CotangentStill section 4.6TangentDefine tangent in terms of sine and cosine

Where is tangent undefined?

y = Tan x

Tangent CurveSo far, we have the curve and 3 key pointsLast two key points come from the midpoints between our asymptotes and the midpointBetween and 0 and between and 0

and

y = Tan x

y =Tan xx und.

und.

00

-11

1-1For variations of the tangent curve

Asymptotes are found by using:

A1. bx c = A2. bx c =

Midpt. =

Key Pts: and

y = 2Tan 2xy =2Tan 2xx und. und.

bx c =

bx c =

2x=

2x =

x =

x =

y = 2Tan 2x

y =2Tan 2xx und. und.00

-22

Midpt =

K.P. = =

K.P. = =

= 0y = 4Tany =4Tan x und. und.00

-44

y = 4Tany =4Tan x und. und.00

-44

Cotangent CurveCotangent curve is very similar to the tangent curve. Only difference is asymptotes

bx c = 0bx c =

0 and are where Cot is undefinedy = 2Cotx und. und.0

2-2

2Cot

x und. und.0

2-2

y = 2Cot

2Cot

x und. und.0

3-3

y = 3 Cot

3Cot