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Graphs of other Trig Functions

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

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Graphs of other Trig Functions

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  1. Graphs of other Trig Functions Section 4.6

  2. 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

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

  4. y = Csc x → y = Sin x 1 -1 Cosecant Curve

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

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

  7. 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. Secant Curve

  8. y = Sec 2x → y = Cos 2x 1 -1 Secant Curve

  9. y = Sec x → y = Cos x 1 -1 Secant Curve

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

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

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

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

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

  15. Graph of Tangent and Cotangent Still section 4.6

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

  17. y = Tan x

  18. 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 Tangent Curve

  19. y = Tan x x 0 y =Tan x und. -1 0 1 und. 1 -1

  20. For variations of the tangent curve • Asymptotes are found by using: A1. bx – c = A2. bx – c = • Midpt. = • Key Pts: and

  21. y = 2Tan 2x x y =2Tan 2x und. und. bx – c = bx – c = 2x = 2x= x = x =

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

  23. y = 4Tan x 0 y =4Tan und. -4 0 4 und.

  24. y = 4Tan x 0 y =4Tan und. -4 0 4 und.

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

  26. y = 2Cot x π und. 2 0 -2 und. 2Cot

  27. y = 2Cot x π 2Cot und. 2 0 -2 und.

  28. y = 3Cot x 3Cot und. 3 0 -3 und.

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