1. [latex]\\sin t=-\\frac{\\sqrt{2}}{2},\\cos t=\\frac{\\sqrt{2}}{2},\\tan t=-1,\\sec t=\\sqrt{2},\\csc t=-\\sqrt{2},\\cot t=-1[\/latex]\n
2. [latex]\\begin{array}{l}\\sin \\frac{\\pi }{3}=\\frac{\\sqrt{3}}{2}\\\\ \\cos \\frac{\\pi }{3}=\\frac{1}{2}\\\\ \\tan \\frac{\\pi }{3}=\\sqrt{3}\\\\ \\sec \\frac{\\pi }{3}=2\\\\ \\csc \\frac{\\pi }{3}=\\frac{2\\sqrt{3}}{3}\\\\ \\cot \\frac{\\pi }{3}=\\frac{\\sqrt{3}}{3}\\end{array}[\/latex]\n
3. [latex]\\sin \\left(\\frac{-7\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2},\\cos \\left(\\frac{-7\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2},\\tan \\left(\\frac{-7\\pi }{4}\\right)=1[\/latex],\n[latex]\\sec \\left(\\frac{-7\\pi }{4}\\right)=\\sqrt{2},\\csc \\left(\\frac{-7\\pi }{4}\\right)=\\sqrt{2},\\cot \\left(\\frac{-7\\pi }{4}\\right)=1[\/latex]\n
4. [latex]-\\sqrt{3}[\/latex]\n
5. [latex]-2[\/latex]\n
6. [latex]\\sin t[\/latex]\n
7. [latex]\\cos t=-\\frac{8}{17},\\sin t=\\frac{15}{17},\\tan t=-\\frac{15}{8}[\/latex]\n[latex]\\csc t=\\frac{17}{15},\\cot t=-\\frac{8}{15}[\/latex]\n
8. [latex]\\begin{array}{l}\\sin t=-1,\\cos t=0,\\tan t=\\text{Undefined}\\\\ \\sec t=\\text{\\hspace{0.17em}Undefined,}\\csc t=-1,\\cot t=0\\end{array}[\/latex]\n
9. [latex]\\sec t=\\sqrt{2},\\csc t=\\sqrt{2},\\tan t=1,\\cot t=1[\/latex]\n
10. [latex]\\approx -2.414[\/latex]\n
1. Yes, when the reference angle is [latex]\\frac{\\pi }{4}[\/latex] and the terminal side of the angle is in quadrants I and III. Thus, at [latex]x=\\frac{\\pi }{4},\\frac{5\\pi }{4}[\/latex], the sine and cosine values are equal.<\/p>\n
3. Substitute the sine of the angle in for [latex]y[\/latex] in the Pythagorean Theorem [latex]{x}^{2}+{y}^{2}=1[\/latex]. Solve for [latex]x[\/latex] and take the negative solution.<\/p>\n
5. The outputs of tangent and cotangent will repeat every [latex]\\pi [\/latex] units.\n
7. [latex]\\frac{2\\sqrt{3}}{3}[\/latex]\n
9. [latex]\\sqrt{3}[\/latex]\n
11. [latex]\\sqrt{2}[\/latex]\n
13. 1<\/p>\n
15. 2<\/p>\n
17. [latex]\\frac{\\sqrt{3}}{3}[\/latex]\n
19. [latex]-\\frac{2\\sqrt{3}}{3}[\/latex]\n
21. [latex]\\sqrt{3}[\/latex]\n
23. [latex]-\\sqrt{2}[\/latex]\n
25. \u22121<\/p>\n
27. \u22122<\/p>\n
29. [latex]-\\frac{\\sqrt{3}}{3}[\/latex]\n
31. 2<\/p>\n
33. [latex]\\frac{\\sqrt{3}}{3}[\/latex]\n
35. \u22122<\/p>\n
37. \u22121<\/p>\n
39. If [latex]\\sin t=-\\frac{2\\sqrt{2}}{3},\\sec t=-3,\\csc t=-\\frac{3\\sqrt{2}}{4},\\tan t=2\\sqrt{2},\\cot t=\\frac{\\sqrt{2}}{4}[\/latex]\n
41. [latex]\\sec t=2,\\csc t=\\frac{2\\sqrt{3}}{3},\\tan t=\\sqrt{3},\\cot t=\\frac{\\sqrt{3}}{3}[\/latex]\n
43. [latex]-\\frac{\\sqrt{2}}{2}[\/latex]\n
45. 3.1<\/p>\n
47. 1.4<\/p>\n
49. [latex]\\sin t=\\frac{\\sqrt{2}}{2},\\cos t=\\frac{\\sqrt{2}}{2},\\tan t=1,\\cot t=1,\\sec t=\\sqrt{2},\\csc t=\\sqrt{2}[\/latex]\n
51. [latex]\\sin t=-\\frac{\\sqrt{3}}{2},\\cos t=-\\frac{1}{2},\\tan t=\\sqrt{3},\\cot t=\\frac{\\sqrt{3}}{3},\\sec t=-2,\\csc t=-\\frac{2\\sqrt{3}}{3}[\/latex]\n
53. \u20130.228<\/p>\n
55. \u20132.414<\/p>\n
57. 1.414<\/p>\n
59. 1.540<\/p>\n
61. 1.556<\/p>\n
63. [latex]\\sin \\left(t\\right)\\approx 0.79[\/latex]\n
65. [latex]\\csc t\\approx 1.16[\/latex]\n
67. even<\/p>\n
69. even<\/p>\n
71. [latex]\\frac{\\sin t}{\\cos t}=\\tan t[\/latex]\n
73. 13.77 hours, period: [latex]1000\\pi [\/latex]\n
75. 7.73 inches<\/p>\n\n","rendered":"
1. [latex]\\sin t=-\\frac{\\sqrt{2}}{2},\\cos t=\\frac{\\sqrt{2}}{2},\\tan t=-1,\\sec t=\\sqrt{2},\\csc t=-\\sqrt{2},\\cot t=-1[\/latex]\n<\/p>\n
2. [latex]\\begin{array}{l}\\sin \\frac{\\pi }{3}=\\frac{\\sqrt{3}}{2}\\\\ \\cos \\frac{\\pi }{3}=\\frac{1}{2}\\\\ \\tan \\frac{\\pi }{3}=\\sqrt{3}\\\\ \\sec \\frac{\\pi }{3}=2\\\\ \\csc \\frac{\\pi }{3}=\\frac{2\\sqrt{3}}{3}\\\\ \\cot \\frac{\\pi }{3}=\\frac{\\sqrt{3}}{3}\\end{array}[\/latex]\n<\/p>\n
3. [latex]\\sin \\left(\\frac{-7\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2},\\cos \\left(\\frac{-7\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2},\\tan \\left(\\frac{-7\\pi }{4}\\right)=1[\/latex],
\n[latex]\\sec \\left(\\frac{-7\\pi }{4}\\right)=\\sqrt{2},\\csc \\left(\\frac{-7\\pi }{4}\\right)=\\sqrt{2},\\cot \\left(\\frac{-7\\pi }{4}\\right)=1[\/latex]\n<\/p>\n
4. [latex]-\\sqrt{3}[\/latex]\n<\/p>\n
5. [latex]-2[\/latex]\n<\/p>\n
6. [latex]\\sin t[\/latex]\n<\/p>\n
7. [latex]\\cos t=-\\frac{8}{17},\\sin t=\\frac{15}{17},\\tan t=-\\frac{15}{8}[\/latex]
\n[latex]\\csc t=\\frac{17}{15},\\cot t=-\\frac{8}{15}[\/latex]\n<\/p>\n
8. [latex]\\begin{array}{l}\\sin t=-1,\\cos t=0,\\tan t=\\text{Undefined}\\\\ \\sec t=\\text{\\hspace{0.17em}Undefined,}\\csc t=-1,\\cot t=0\\end{array}[\/latex]\n<\/p>\n
9. [latex]\\sec t=\\sqrt{2},\\csc t=\\sqrt{2},\\tan t=1,\\cot t=1[\/latex]\n<\/p>\n
10. [latex]\\approx -2.414[\/latex]\n<\/p>\n
1. Yes, when the reference angle is [latex]\\frac{\\pi }{4}[\/latex] and the terminal side of the angle is in quadrants I and III. Thus, at [latex]x=\\frac{\\pi }{4},\\frac{5\\pi }{4}[\/latex], the sine and cosine values are equal.<\/p>\n
3. Substitute the sine of the angle in for [latex]y[\/latex] in the Pythagorean Theorem [latex]{x}^{2}+{y}^{2}=1[\/latex]. Solve for [latex]x[\/latex] and take the negative solution.<\/p>\n
5. The outputs of tangent and cotangent will repeat every [latex]\\pi[\/latex] units.\n<\/p>\n
7. [latex]\\frac{2\\sqrt{3}}{3}[\/latex]\n<\/p>\n
9. [latex]\\sqrt{3}[\/latex]\n<\/p>\n
11. [latex]\\sqrt{2}[\/latex]\n<\/p>\n
13. 1<\/p>\n
15. 2<\/p>\n
17. [latex]\\frac{\\sqrt{3}}{3}[\/latex]\n<\/p>\n
19. [latex]-\\frac{2\\sqrt{3}}{3}[\/latex]\n<\/p>\n
21. [latex]\\sqrt{3}[\/latex]\n<\/p>\n
23. [latex]-\\sqrt{2}[\/latex]\n<\/p>\n
25. \u22121<\/p>\n
27. \u22122<\/p>\n
29. [latex]-\\frac{\\sqrt{3}}{3}[\/latex]\n<\/p>\n
31. 2<\/p>\n
33. [latex]\\frac{\\sqrt{3}}{3}[\/latex]\n<\/p>\n
35. \u22122<\/p>\n
37. \u22121<\/p>\n
39. If [latex]\\sin t=-\\frac{2\\sqrt{2}}{3},\\sec t=-3,\\csc t=-\\frac{3\\sqrt{2}}{4},\\tan t=2\\sqrt{2},\\cot t=\\frac{\\sqrt{2}}{4}[\/latex]\n<\/p>\n
41. [latex]\\sec t=2,\\csc t=\\frac{2\\sqrt{3}}{3},\\tan t=\\sqrt{3},\\cot t=\\frac{\\sqrt{3}}{3}[\/latex]\n<\/p>\n
43. [latex]-\\frac{\\sqrt{2}}{2}[\/latex]\n<\/p>\n
45. 3.1<\/p>\n
47. 1.4<\/p>\n
49. [latex]\\sin t=\\frac{\\sqrt{2}}{2},\\cos t=\\frac{\\sqrt{2}}{2},\\tan t=1,\\cot t=1,\\sec t=\\sqrt{2},\\csc t=\\sqrt{2}[\/latex]\n<\/p>\n
51. [latex]\\sin t=-\\frac{\\sqrt{3}}{2},\\cos t=-\\frac{1}{2},\\tan t=\\sqrt{3},\\cot t=\\frac{\\sqrt{3}}{3},\\sec t=-2,\\csc t=-\\frac{2\\sqrt{3}}{3}[\/latex]\n<\/p>\n
53. \u20130.228<\/p>\n
55. \u20132.414<\/p>\n
57. 1.414<\/p>\n
59. 1.540<\/p>\n
61. 1.556<\/p>\n
63. [latex]\\sin \\left(t\\right)\\approx 0.79[\/latex]\n<\/p>\n
65. [latex]\\csc t\\approx 1.16[\/latex]\n<\/p>\n
67. even<\/p>\n
69. even<\/p>\n
71. [latex]\\frac{\\sin t}{\\cos t}=\\tan t[\/latex]\n<\/p>\n
73. 13.77 hours, period: [latex]1000\\pi[\/latex]\n<\/p>\n
75. 7.73 inches<\/p>\n\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t