College Trigonometry, 2011a

10.3 The Six Circular Functions and Fundamental Identities 767
35. csc(78.95 ◦ ) ≈ 1.019 36. tan(−2.01) ≈ 2.129
37. cot(392.994) ≈ 3.292 38. sec(207 ◦ ) ≈−1.122
39. csc(5.902) ≈−2.688 40. tan(39.672 ◦ ) ≈ 0.829
41. cot(3 ◦ ) ≈ 19.081 42. sec(0.45) ≈ 1.111
43. tan(θ) = √ 3whenθ = π 3
+ πk for any integer k
44. sec(θ) =2whenθ = π 3 +2πk or θ = 5π 3
+2πk for any integer k
45. csc(θ) =−1 whenθ = 3π 2
+2πk for any integer k.
√
3
46. cot(θ) =
3 when θ = π + πk for any integer k
3
47. tan(θ) =0whenθ = πk for any integer k
48. sec(θ) =1whenθ =2πk for any integer k
49. csc(θ) =2whenθ = π 6 +2πk or θ = 5π 6
+2πk for any integer k.
50. cot(θ) =0whenθ = π 2
+ πk for any integer k
51. tan(θ) =−1 whenθ = 3π 4
+ πk for any integer k
52. sec(θ) = 0 never happens
53. csc(θ) =− 1 2
never happens
54. sec(θ) =−1 whenθ = π +2πk =(2k +1)π for any integer k
55. tan(θ) =− √ 3whenθ = 2π 3
+ πk for any integer k
56. csc(θ) =−2 whenθ = 7π 6
+2πk or θ =
11π
6
+2πk for any integer k
57. cot(θ) =−1 whenθ = 3π 4
+ πk for any integer k
58. cot(t) =1whent = π 4
+ πk for any integer k
59. tan(t) =
√
3
3 when t = π + πk for any integer k
6