π π π tan ⎛ 3x + ⎞ − csc ⎛ − 1 + ⎞ 24. x y 26. =− = y ⎜ ⎟ 2 ⎜ 2 4 ⎟ ⎝ ⎠ ⎝ ⎠ Begin with the graph of = tan and apply the = csc and apply the y x Begin with the graph of y x following transformations: following transformations: π π ⎡ = ⎛ + ⎞⎤ 1) Shift left units tan y x π π 1) Shift left units ⎡ = csc ⎛ + ⎞⎤ y x 2 ⎢ ⎜ ⎢ ⎜ 4 2 ⎟⎥ 4 ⎟⎥ ⎝ ⎠ ⎝ ⎠ π ⎡ ⎛ ⎞⎤ 2) Horizontally compress by a factor of 1 2) Reflect about the = csc − + y-axis y x 3 ⎢ ⎜ ⎟⎥ 4 ⎝ ⎠ π ⎡ ⎛ ⎞⎤ = tan 3x + y 2 ⎢ ⎜ ⎟⎥ 2 3) Horizontally compress by a factor of ⎝ ⎠ π π ⎛ 1 ⎞ ⎡ ⎛ π ⎞⎤ 3) Reflect about the =− tan + x-axis y x ⎢ ⎜ ⎟⎥ = − π 2 csc + y x ⎡ ⎤ ⎢ ⎝ ⎠ ⎜ 2 4 ⎟⎥ ⎝ ⎠ 3) Reflect about the x-axis ⎡ ⎛ 1 π ⎞⎤ ⎛ π ,1⎞ π + ⎟⎥ x ⎢ = − csc ⎜ − y ⎜12 ⎟ ⎢ ⎝ 2 4 ⎠⎥ ⎣ ⎦ ⎝ ⎠ ⎛ π , −1⎞ ⎜ 4 ⎟ ⎝ ⎠ 25. (2π ) π = − + sec y x = sec and apply the y x Begin with the graph of following transformations: ( π ⎡ = + π 1) Shift left units sec y x )⎤ (t ) 27. ≥ 0 t = 120 sin ⎛ 30π − I t π ⎞ , ⎣ ⎦ ⎜ ⎟ 3
24. y =− tan ⎛ 3x + π ⎞ 26. y = − csc ⎛ − 1 π x + π ⎞ ⎜ 2 ⎟ ⎜ 2 4 ⎟ ⎝ ⎠ Begin with the graph of y = tan x and apply the ⎝ ⎠ Begin with the graph of y = csc x and apply the following transformations: 1) Shift left π units ⎡ y = tan ⎛ x + π ⎞⎤ following transformations: 1) Shift left π units ⎡ y = csc ⎛ x + π ⎞⎤ 2 ⎢ ⎜ 2 ⎟⎥ 4 ⎢ ⎜ 4 ⎟⎥ ⎝ ⎠ ⎝ ⎠ 2) Horizontally compress by a factor of 1 ⎡ ⎛ π ⎞⎤ 2) Reflect about the y-axis y = csc − x + 3 ⎢ ⎜ 4 ⎟⎥ ⎝ ⎠ ⎡ ⎛ π ⎞⎤ y = tan 3x + ⎢ ⎜ 2 ⎟⎥ 2 ⎝ ⎠ 3) Horizontally compress by a factor of π ⎡ ⎛ π ⎞⎤ 3) Reflect about the x-axis y =− tan x + ⎛ 1 π ⎞ ⎢ ⎜ 2 ⎟⎥ ⎡ y = csc − ⎤ π x + ⎝ ⎠ ⎢ ⎜ 2 4 ⎟⎥ ⎝ ⎠ 3) Reflect about the x-axis ⎡ ⎛ 1 π ⎞⎤ ⎛ π ,1⎞ ⎢ y = − csc ⎜ − π x + ⎟⎥ ⎜12 ⎟ ⎢ ⎝ 2 4 ⎠⎥ ⎝ ⎠ ⎣ ⎦ ⎛ π , −1⎞ ⎜ 4 ⎟ ⎝ ⎠ 25. y = − sec (2π x + π ) Begin with the graph of y = sec x and apply the following transformations: 1) Shift left π units ⎡ y = sec ( x + π )⎤ 27. I (t ) = 120 sin ⎛ 30π t − π ⎞ , t ≥ 0 ⎣ ⎦ ⎜ 3 ⎟
62514-0132318806_ISM_02-1.docx