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Graphs of other Trig Functions Section 4.6

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Cosecant Curve 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

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Cosecant Curve Drawing the cosecant curve 1) Draw the reciprocal curve 2) Add vertical asymptotes wherever curve goes through horizontal axis 3) “Hills” become “Valleys” and “Valleys” become “Hills”

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Cosecant Curve y = Csc x→ y = Sin x 1

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Cosecant Curve y = 3 Csc (4x – π)→ y = 3 Sin (4x – π) a = 3b = 4 Per. = dis. = c = π P.S. = -3 3

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Cosecant Curve y = -2 Csc 4x + 2→ y = -2 Sin 4x + 2 2 4

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Secant Curve What 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.

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Secant Curve y = Sec 2x→ y = Cos 2x 1

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Secant Curve y = Sec x→ y = Cos x 1

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Graph these curves 1) y = 3 Csc (πx – 2π) 2) y = 2 Sec (x + ) 3) y = ½ Csc (x - ) 4) y = -2 Sec (4x + 2π)

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y = 3Csc (πx – 2π)→ y = 3 Sin (π x – 2π) -3 3

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

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y = ½ Csc (x - )→ y = ½ Csc (x - ) - ½ ½

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

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Graph of Tangent and Cotangent Still section 4.6

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Tangent Define tangent in terms of sine and cosine Where is tangent undefined?

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y = Tan x

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Tangent Curve So far, we have the curve and 3 key points Last two key points come from the midpoints between our asymptotes and the midpoint ◦Between and 0 and between and 0 → and

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y = Tan x x und. 0 0 1 1

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For variations of the tangent curve 1) Asymptotes are found by using: A1. bx – c = A2. bx – c = 2) Midpt. = 3) Key Pts: and

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y = 2Tan 2x x und. bx – c = 2x= x =

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y = 2Tan 2x x und. 0 0 -22 Midpt = K.P. = = = 0

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y = 4Tan x und. 0 0 -44

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y = 4Tan x und. 0 0 -44

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Cotangent Curve Cotangent curve is very similar to the tangent curve. Only difference is asymptotes bx – c = 0bx – c = π → 0 and π are where Cot is undefined

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y = 2Cot x und. 0 π 2-2 2Cot

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x und. 0 π 2-2 y = 2Cot 2Cot

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x und. 03-3 y = 3 Cot 3Cot

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Graph the following curves: y = 2 Cos ( + ) + 2 y = 2 Sin ( + π ) + 1 y = 5 Tan (4x – π )

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y = 2 Cos ( + ) + 2 a = 2b = Per. = dis. = c = P.S. = 2 4 d =

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y = 2 Sin ( + π ) + 1 a = 2b = Per. = dis. = c = P.S. = 1 3 d =

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y = 5Tan (4x – π) 5Tan (4x – π) x und. 0-55

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Graph the following curves: y = -3 Sec (x + ) y = -2 Csc (x - ) y = ½ Cot (x – )

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y = -3 Sec (x + ) -3 Sec ( x + ) -3 3

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y = -2 Csc (x - )→ y = -2 Csc (x - ) - 2 2

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x und. 0½- ½ y = ½ Cot ½ Cot

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12-2 Trigonometric Functions of Acute Angles

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