60 63.18o 86. a. b. = = 0.18o (0.18)(60 ') 10.8 ' = = 0.8 ' (0.8)(60 ") 48" Thus, 63.18o = 63o10 ' 48" = + + ≈ 32o 20 ' 35" 32 20 35 32.34o 6 θ Terminal side of in Quadrant III implies 81. = r θ sin < 0 cscθ < 0 θ = 30º 2 θ or = π 87. < < cosθ 0 secθ θ θ 0 tan > 0 cot = = ⋅ π = π ≈ 2 1.047 s rθ > 0 feet 6 3 θ θ 82. cosθ > 0, tan < 0 ; lies in quadrant IV. (2)2 = 1 ⋅ = 1 ⋅ ⋅ π = π ≈ 1.047 square A r 2θ feet 2 2 6 3 ⎞ 1 2 2 83. = − , θ θ 88. In 30 minutes: = 8 inches, = 180º or = π P r ⎛ ⎜ 3 3 ⎟ = = 8 ⋅ π= 8π≈ 25.13 inches s rθ ⎝ ⎠ 2π = sin 2 2 ; t θ = 120º or In 20 minutes: csc = 1 = 3 ⋅ 2 = 3 t θ = 3 2 = 8 inches, r ⎛ ⎞ 3 2 2 2 2 2 4 ⎜ 3 ⎟ = = 8 ⋅ 2π = 16π ≈ 16.76 inches s rθ ⎝ ⎠ 3 3
86. a. b. 32o 20 ' 35" = 32 + 20 + 35 ≈ 32.34o 60 63.18o 0.18o = (0.18)(60 ') = 10.8 ' 0.8 ' = (0.8)(60 ") = 48" Thus, 63.18o = 63o10 ' 48" 81. Terminal side of θ in Quadrant III implies sin θ < 0 cscθ < 0 87. r = 2 θ = 30º or θ = π 6 cosθ < 0 secθ < 0 tan θ > 0 cot θ > 0 82. cosθ > 0, tan θ < 0 ; θ lies in quadrant IV. s = rθ = 2 ⋅ π = π ≈ 1.047 feet 6 3 A = 1 ⋅ r 2θ = 1 ⋅ (2)2 ⋅ π = π ≈ 1.047 square feet 2 2 6 3 83. ⎛ 1 2 2 ⎞ P = − , 88. In 30 minutes: r = 8 inches, θ = 180º or θ = π ⎜ 3 3 ⎟ s = rθ = 8 ⋅ π= 8π≈ 25.13 inches ⎝ ⎠ 2π sin t = 2 2 ; csc t = 1 = 3 ⋅ 2 = 3 2 In 20 minutes: r = 8 inches, θ = 120º or θ = 3 3 ⎛ 2 2 ⎞ 2 2 2 4 ⎜ 3 ⎟ s = rθ = 8 ⋅ 2π = 16π ≈ 16.76 inches ⎝ ⎠ 3 3
62514-0132318806_ISM_02-1.docx