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