= b. When 4 , the coordinate on the unit t 15. csc 450º = csc(360º + 90º ) = csc 90º = 1 circle is approximately (−0.7, −0.8) . Thus, ≈ −0.7 ≈ cot 4 0.9 sin 4 ≈ −0.8 ≈ ≈ csc 4 1 = + = = −1 16. sec 540º sec(360º 180º ) sec180º cos 4 ≈ −0.7 −1.3 −0.8 = + + = = 17. cot 390º cot(180º 180º 30º ) cot 30º ≈ −0.8 ≈ tan 4 ≈ ≈ sec 4 1 3 1.1 −1.4 = + = = −0.7 18. sec 420º sec(360º 60º ) sec 60º 2 −0.7 33π −0.8 ⎛ π ⎞ ⎛ π ⎞ Set the calculator on RADIAN mode: cos ⎜ = + 19. cos 8π + 4 ⋅ ⎜ ⎟ = ⎟ 2π cos 4 ⎝ 4 = cos π 4 ⎠ ⎝ ⎠ 4 2 20. 2 129 131. Answers will vary. – sin 9π = sin ⎛ π + 2π ⎞ = sin π = 2 = 4 ⎜ 4 ⎟ 4 2 (21π) (0) tan = tan(0 + 21π) = tan = 0 ⎝ Section 2.3 ⎧ | 1 ⎫ x x ⎠ 1. All real numbers except − 1 ; 21. ⎨ ≠− ⎬ ⎩ ⎭ 2 2 9π ⎛ π ⎞ ⎛ π ⎞ 22. csc ⎜ + csc 4π + 2 ⋅ ⎟ = 2π ⎟ = ⎜ csc = csc π 2. even ⎝ 2 2 2 3. False = 1 ⎠ ⎝ 2 ⎠ 4. True π 5. 2π , 23. = ⎛ π + ⎞ = ⎛ π + ⋅ ⎞ sec 17π sec 4π sec 2 2π ⎜ ⎟ ⎜ ⎟ 4 4 4 ⎝ ⎠ ⎝ ⎠ π 6. All real number, except odd multiples of = sec π 2 4 { is, | −1 ≤ ≤ 1} or y y 7. All real numbers between −1 and 1, inclusive. [−1, 1] .
b. When t = 4 , the coordinate on the unit circle is approximately (−0.7, −0.8) . Thus, 15. csc 450º = csc(360º + 90º ) = csc 90º = 1 sin 4 ≈ −0.8 cos 4 ≈ −0.7 tan 4 ≈ −0.8 ≈ 1.1 csc 4 ≈ 1 ≈ −1.3 −0.8 sec 4 ≈ 1 ≈ −1.4 −0.7 cot 4 ≈ −0.7 ≈ 0.9 16. sec 540º = sec(360º + 180º ) = sec180º = −1 17. cot 390º = cot(180º + 180º + 30º ) = cot 30º = 3 18. sec 420º = sec(360º + 60º ) = sec 60º = 2 −0.7 −0.8 33π ⎛ π ⎞ ⎛ π ⎞ Set the calculator on RADIAN mode: 19. cos = cos ⎜ + 8π ⎟ = cos ⎜ + 4 ⋅ 2π ⎟ 4 ⎝ 4 ⎠ ⎝ 4 ⎠ = cos π 4 129 – 131. Answers will vary. 20. = 2 2 sin 9π = sin ⎛ π + 2π ⎞ = sin π = 2 4 ⎜ 4 ⎟ 4 2 Section 2.3 1. All real numbers except − 1 ; ⎧ x | x 1 ⎫ 21. ⎝ ⎠ tan (21π) = tan(0 + 21π) = tan (0) = 0 ⎨ ≠− ⎬ 2 ⎩ 2 ⎭ 9π ⎛ π ⎞ ⎛ π ⎞ 22. csc = csc ⎜ + 4π ⎟ = csc ⎜ + 2 ⋅ 2π ⎟ 2. even 3. False 4. True 2 ⎝ 2 ⎠ ⎝ 2 ⎠ = csc π 2 = 1 5. 2π , π 23. sec 17π = sec ⎛ π + 4π ⎞ = sec ⎛ π + 2 ⋅ 2π ⎞ 4 ⎜ 4 ⎟ ⎜ 4 ⎟ 6. All real number, except odd multiples of π 2 ⎝ ⎠ ⎝ ⎠ = sec π 4 7. All real numbers between −1 and 1, inclusive. is, { y | −1 ≤ y ≤ 1} or [−1, 1] .
62514-0132318806_ISM_02-1.docx