{"id":338,"date":"2026-02-16T20:52:42","date_gmt":"2026-02-16T20:52:42","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/?post_type=chapter&#038;p=338"},"modified":"2026-02-17T18:11:11","modified_gmt":"2026-02-17T18:11:11","slug":"trigonometric-functions-get-stronger-answer-key","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/trigonometric-functions-get-stronger-answer-key\/","title":{"raw":"Trigonometric Functions: Get Stronger Answer Key","rendered":"Trigonometric Functions: Get Stronger Answer Key"},"content":{"raw":"<h2>Angles<\/h2>\r\n3.\u00a0Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.\r\n\r\n5.\u00a0Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.\r\n\r\n7.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003508\/CNX_Precalc_Figure_05_01_203.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/>\r\n\r\n9.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003510\/CNX_Precalc_Figure_05_01_205.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/>\r\n\r\n11.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003513\/CNX_Precalc_Figure_05_01_207.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/>\r\n\r\n13.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003515\/CNX_Precalc_Figure_05_01_209.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/>\r\n\r\n15.\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003517\/CNX_Precalc_Figure_05_01_211.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/>\r\n\r\n17.\u00a0240\u00b0<span id=\"fs-id1165133402094\">\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003520\/CNX_Precalc_Figure_05_01_213.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/><\/span>\r\n\r\n19.\u00a0[latex]\\frac{4\\pi }{3}[\/latex]<span id=\"fs-id1165135628464\">\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003523\/CNX_Precalc_Figure_05_01_215.jpg\" alt=\"Graph of a circle showing the equivalence of two angles.\" \/><\/span>\r\n\r\n21.\u00a0[latex]\\frac{2\\pi }{3}[\/latex]<span id=\"fs-id1165134374733\">\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003525\/CNX_Precalc_Figure_05_01_217.jpg\" alt=\"Graph of a circle showing the equivalence of two angles.\" \/><\/span>\r\n\r\n22. [latex]s=\\frac{7\\pi}{3}\\approx 7.33[\/latex]\r\n\r\n23. [latex]\\frac{7\\pi }{2}\\approx 11.00{\\text{ in}}^{2}[\/latex]\r\n\r\n24. [latex]s=\\frac{9\\pi}{5}\\approx 5.65[\/latex]\r\n\r\n25.\u00a0[latex]\\frac{81\\pi }{20}\\approx 12.72{\\text{ cm}}^{2}[\/latex]\r\n\r\n27.\u00a020\u00b0\r\n\r\n29.\u00a060\u00b0\r\n\r\n31.\u00a0\u221275\u00b0\r\n\r\n33.\u00a0[latex]\\frac{\\pi }{2}[\/latex] radians\r\n\r\n35.\u00a0[latex]-3\\pi [\/latex] radians\r\n\r\n37.\u00a0[latex]\\pi [\/latex] radians\r\n\r\n39.\u00a0[latex]\\frac{5\\pi }{6}[\/latex] radians\r\n\r\n41.\u00a0[latex]\\frac{5.02\\pi }{3}\\approx 5.26[\/latex] miles\r\n\r\n45.\u00a0[latex]\\frac{21\\pi }{10}\\approx 6.60[\/latex] meters\r\n\r\n47.\u00a0104.7198 cm2\r\n\r\n49.\u00a00.7697 in2\r\n\r\n51.\u00a0250\u00b0\r\n\r\n53.\u00a0320\u00b0\r\n\r\n55.\u00a0[latex]\\frac{4\\pi }{3}[\/latex]\r\n\r\n57.\u00a0[latex]\\frac{8\\pi }{9}[\/latex]\r\n\r\n59.\u00a01320 rad 210.085 RPM\r\n\r\n61.\u00a07 in.\/s, 4.77 RPM, 28.65 deg\/s\r\n\r\n65.\u00a0[latex]5.76[\/latex]\u00a0miles\r\n\r\n67.\u00a0[latex]120^\\circ [\/latex]\r\n\r\n73.\u00a011.5 inches\r\n\r\n74. [latex]52^\\circ 22' 30''[\/latex]\r\n\r\n75. [latex]-73^\\circ 15' 0''[\/latex]\r\n\r\n76. 7[latex]140^\\circ 0' 28.8''[\/latex]\r\n\r\n77. [latex]38.2567^\\circ[\/latex]\r\n\r\n78. [latex]72.0100^\\circ[\/latex]\r\n\r\n79. [latex]-19.5000^\\circ[\/latex]\r\n\r\n80. Complement: [latex]62^\\circ[\/latex], Supplement: [latex]152^\\circ[\/latex]\r\n\r\n81. Complement: [latex]47^\\circ 41' 24''[\/latex], Supplement: [latex]137^\\circ 41' 24''[\/latex]\r\n\r\n82. Complement: No complement exists, Supplement: [latex]68^\\circ[\/latex]\r\n\r\n83. Complement: [latex]\\frac{3\\pi}{8}[\/latex], Supplement: [latex]\\frac{7\\pi}{8}[\/latex]\r\n<h1>Unit Circle: Sine and Cosine Functions<\/h1>\r\n2. On the unit circle, the coordinates of a point corresponding to an angle t are [latex](\\cos t,\\ \\sin t)[\/latex]. The x-coordinate represents [latex]\\cos t[\/latex] and the y-coordinate represents [latex]\\sin t[\/latex].\r\n\r\n3.\u00a0Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle, [latex]t[\/latex], formed by the terminal side of the angle [latex]t[\/latex] and the horizontal axis.\r\n\r\n5.\u00a0The sine values are equal.\r\n\r\n7. I\r\n\r\n9. IV\r\n\r\n11.\u00a0[latex]\\frac{\\sqrt{3}}{2}[\/latex]\r\n\r\n13.\u00a0[latex]\\frac{1}{2}[\/latex]\r\n\r\n15.\u00a0[latex]\\frac{\\sqrt{2}}{2}[\/latex]\r\n\r\n17. 0\r\n\r\n21.\u00a0[latex]\\frac{\\sqrt{3}}{2}[\/latex]\r\n\r\n23.\u00a0[latex]60^\\circ [\/latex]\r\n\r\n27.\u00a0[latex]45^\\circ [\/latex]\r\n\r\n29.\u00a0[latex]\\frac{\\pi }{3}[\/latex]\r\n\r\n31.\u00a0[latex]\\frac{\\pi }{3}[\/latex]\r\n\r\n35.\u00a0[latex]60^\\circ [\/latex], Quadrant IV, [latex]\\text{sin}\\left(300^\\circ \\right)=-\\frac{\\sqrt{3}}{2},\\cos \\left(300^\\circ \\right)=\\frac{1}{2}[\/latex]\r\n\r\n37.\u00a0[latex]45^\\circ [\/latex], Quadrant II, [latex]\\text{sin}\\left(135^\\circ \\right)=\\frac{\\sqrt{2}}{2}[\/latex], [latex]\\cos \\left(135^\\circ \\right)=-\\frac{\\sqrt{2}}{2}[\/latex]\r\n\r\n43.\u00a0[latex]\\frac{\\pi }{6}[\/latex], Quadrant III, [latex]\\text{sin}\\left(\\frac{7\\pi }{6}\\right)=-\\frac{1}{2}[\/latex], [latex]\\text{cos}\\left(\\frac{7\\pi }{6}\\right)=-\\frac{\\sqrt{3}}{2}[\/latex]\r\n\r\n45.\u00a0[latex]\\frac{\\pi }{4}[\/latex], Quadrant II, [latex]\\text{sin}\\left(\\frac{3\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2}[\/latex], [latex]\\cos \\left(\\frac{4\\pi }{3}\\right)=-\\frac{\\sqrt[]{2}}{2}[\/latex]\r\n\r\n51.\u00a0[latex]\\frac{\\sqrt{77}}{9}[\/latex]\r\n\r\n53.\u00a0[latex]-\\frac{\\sqrt{15}}{4}[\/latex]\r\n\r\n61.\u00a0[latex]\\sin t=\\frac{1}{2},\\cos t=-\\frac{\\sqrt{3}}{2}[\/latex]\r\n\r\n63.\u00a0[latex]\\sin t=-\\frac{\\sqrt{2}}{2},\\cos t=-\\frac{\\sqrt{2}}{2}[\/latex]\r\n\r\n65.\u00a0[latex]\\sin t=\\frac{\\sqrt{3}}{2},\\cos t=-\\frac{1}{2}[\/latex]\r\n\r\n67.\u00a0[latex]\\sin t=-\\frac{\\sqrt{2}}{2},\\cos t=\\frac{\\sqrt{2}}{2}[\/latex]\r\n\r\n69.\u00a0[latex]\\sin t=0,\\cos t=-1[\/latex]\r\n\r\n73.\u00a0[latex]\\sin t=\\frac{1}{2},\\cos t=\\frac{\\sqrt{3}}{2}[\/latex]\r\n\r\n81.\u00a0\u22120.1736\r\n\r\n83.\u00a00.9511\r\n\r\n87.\u00a0\u22120.1392\r\n\r\n89.\u00a0\u22120.7660\r\n<h1>Other Trigonometric Functions<\/h1>\r\n7.\u00a0[latex]\\frac{2\\sqrt{3}}{3}[\/latex]\r\n\r\n13. 1\r\n\r\n19.\u00a0[latex]-\\frac{2\\sqrt{3}}{3}[\/latex]\r\n\r\n21.\u00a0[latex]\\sqrt{3}[\/latex]\r\n\r\n33.\u00a0[latex]\\frac{\\sqrt{3}}{3}[\/latex]\r\n\r\n35.\u00a0\u22122\r\n\r\n39.\u00a0If [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]\r\n\r\n41.\u00a0[latex]\\sec t=2,\\csc t=\\frac{2\\sqrt{3}}{3},\\tan t=\\sqrt{3},\\cot t=\\frac{\\sqrt{3}}{3}[\/latex]\r\n\r\n43.\u00a0[latex]-\\frac{\\sqrt{2}}{2}[\/latex]\r\n\r\n45.\u00a03.1\r\n\r\n47.\u00a01.4\r\n\r\n53.\u00a0\u20130.228\r\n\r\n55.\u00a0\u20132.414\r\n\r\n57.\u00a01.414\r\n\r\n61.\u00a01.556\r\n\r\n73.\u00a013.77 hours, period: [latex]1000\\pi [\/latex]\r\n\r\n75.\u00a07.73 inches","rendered":"<h2>Angles<\/h2>\n<p>3.\u00a0Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.<\/p>\n<p>5.\u00a0Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.<\/p>\n<p>7.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003508\/CNX_Precalc_Figure_05_01_203.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/><\/p>\n<p>9.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003510\/CNX_Precalc_Figure_05_01_205.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/><\/p>\n<p>11.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003513\/CNX_Precalc_Figure_05_01_207.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/><\/p>\n<p>13.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003515\/CNX_Precalc_Figure_05_01_209.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/><\/p>\n<p>15.<br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003517\/CNX_Precalc_Figure_05_01_211.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/><\/p>\n<p>17.\u00a0240\u00b0<span id=\"fs-id1165133402094\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003520\/CNX_Precalc_Figure_05_01_213.jpg\" alt=\"Graph of a circle with an angle inscribed.\" \/><\/span><\/p>\n<p>19.\u00a0[latex]\\frac{4\\pi }{3}[\/latex]<span id=\"fs-id1165135628464\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003523\/CNX_Precalc_Figure_05_01_215.jpg\" alt=\"Graph of a circle showing the equivalence of two angles.\" \/><\/span><\/p>\n<p>21.\u00a0[latex]\\frac{2\\pi }{3}[\/latex]<span id=\"fs-id1165134374733\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/3675\/2018\/09\/27003525\/CNX_Precalc_Figure_05_01_217.jpg\" alt=\"Graph of a circle showing the equivalence of two angles.\" \/><\/span><\/p>\n<p>22. [latex]s=\\frac{7\\pi}{3}\\approx 7.33[\/latex]<\/p>\n<p>23. [latex]\\frac{7\\pi }{2}\\approx 11.00{\\text{ in}}^{2}[\/latex]<\/p>\n<p>24. [latex]s=\\frac{9\\pi}{5}\\approx 5.65[\/latex]<\/p>\n<p>25.\u00a0[latex]\\frac{81\\pi }{20}\\approx 12.72{\\text{ cm}}^{2}[\/latex]<\/p>\n<p>27.\u00a020\u00b0<\/p>\n<p>29.\u00a060\u00b0<\/p>\n<p>31.\u00a0\u221275\u00b0<\/p>\n<p>33.\u00a0[latex]\\frac{\\pi }{2}[\/latex] radians<\/p>\n<p>35.\u00a0[latex]-3\\pi[\/latex] radians<\/p>\n<p>37.\u00a0[latex]\\pi[\/latex] radians<\/p>\n<p>39.\u00a0[latex]\\frac{5\\pi }{6}[\/latex] radians<\/p>\n<p>41.\u00a0[latex]\\frac{5.02\\pi }{3}\\approx 5.26[\/latex] miles<\/p>\n<p>45.\u00a0[latex]\\frac{21\\pi }{10}\\approx 6.60[\/latex] meters<\/p>\n<p>47.\u00a0104.7198 cm2<\/p>\n<p>49.\u00a00.7697 in2<\/p>\n<p>51.\u00a0250\u00b0<\/p>\n<p>53.\u00a0320\u00b0<\/p>\n<p>55.\u00a0[latex]\\frac{4\\pi }{3}[\/latex]<\/p>\n<p>57.\u00a0[latex]\\frac{8\\pi }{9}[\/latex]<\/p>\n<p>59.\u00a01320 rad 210.085 RPM<\/p>\n<p>61.\u00a07 in.\/s, 4.77 RPM, 28.65 deg\/s<\/p>\n<p>65.\u00a0[latex]5.76[\/latex]\u00a0miles<\/p>\n<p>67.\u00a0[latex]120^\\circ[\/latex]<\/p>\n<p>73.\u00a011.5 inches<\/p>\n<p>74. [latex]52^\\circ 22' 30''[\/latex]<\/p>\n<p>75. [latex]-73^\\circ 15' 0''[\/latex]<\/p>\n<p>76. 7[latex]140^\\circ 0' 28.8''[\/latex]<\/p>\n<p>77. [latex]38.2567^\\circ[\/latex]<\/p>\n<p>78. [latex]72.0100^\\circ[\/latex]<\/p>\n<p>79. [latex]-19.5000^\\circ[\/latex]<\/p>\n<p>80. Complement: [latex]62^\\circ[\/latex], Supplement: [latex]152^\\circ[\/latex]<\/p>\n<p>81. Complement: [latex]47^\\circ 41' 24''[\/latex], Supplement: [latex]137^\\circ 41' 24''[\/latex]<\/p>\n<p>82. Complement: No complement exists, Supplement: [latex]68^\\circ[\/latex]<\/p>\n<p>83. Complement: [latex]\\frac{3\\pi}{8}[\/latex], Supplement: [latex]\\frac{7\\pi}{8}[\/latex]<\/p>\n<h1>Unit Circle: Sine and Cosine Functions<\/h1>\n<p>2. On the unit circle, the coordinates of a point corresponding to an angle t are [latex](\\cos t,\\ \\sin t)[\/latex]. The x-coordinate represents [latex]\\cos t[\/latex] and the y-coordinate represents [latex]\\sin t[\/latex].<\/p>\n<p>3.\u00a0Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle, [latex]t[\/latex], formed by the terminal side of the angle [latex]t[\/latex] and the horizontal axis.<\/p>\n<p>5.\u00a0The sine values are equal.<\/p>\n<p>7. I<\/p>\n<p>9. IV<\/p>\n<p>11.\u00a0[latex]\\frac{\\sqrt{3}}{2}[\/latex]<\/p>\n<p>13.\u00a0[latex]\\frac{1}{2}[\/latex]<\/p>\n<p>15.\u00a0[latex]\\frac{\\sqrt{2}}{2}[\/latex]<\/p>\n<p>17. 0<\/p>\n<p>21.\u00a0[latex]\\frac{\\sqrt{3}}{2}[\/latex]<\/p>\n<p>23.\u00a0[latex]60^\\circ[\/latex]<\/p>\n<p>27.\u00a0[latex]45^\\circ[\/latex]<\/p>\n<p>29.\u00a0[latex]\\frac{\\pi }{3}[\/latex]<\/p>\n<p>31.\u00a0[latex]\\frac{\\pi }{3}[\/latex]<\/p>\n<p>35.\u00a0[latex]60^\\circ[\/latex], Quadrant IV, [latex]\\text{sin}\\left(300^\\circ \\right)=-\\frac{\\sqrt{3}}{2},\\cos \\left(300^\\circ \\right)=\\frac{1}{2}[\/latex]<\/p>\n<p>37.\u00a0[latex]45^\\circ[\/latex], Quadrant II, [latex]\\text{sin}\\left(135^\\circ \\right)=\\frac{\\sqrt{2}}{2}[\/latex], [latex]\\cos \\left(135^\\circ \\right)=-\\frac{\\sqrt{2}}{2}[\/latex]<\/p>\n<p>43.\u00a0[latex]\\frac{\\pi }{6}[\/latex], Quadrant III, [latex]\\text{sin}\\left(\\frac{7\\pi }{6}\\right)=-\\frac{1}{2}[\/latex], [latex]\\text{cos}\\left(\\frac{7\\pi }{6}\\right)=-\\frac{\\sqrt{3}}{2}[\/latex]<\/p>\n<p>45.\u00a0[latex]\\frac{\\pi }{4}[\/latex], Quadrant II, [latex]\\text{sin}\\left(\\frac{3\\pi }{4}\\right)=\\frac{\\sqrt{2}}{2}[\/latex], [latex]\\cos \\left(\\frac{4\\pi }{3}\\right)=-\\frac{\\sqrt[]{2}}{2}[\/latex]<\/p>\n<p>51.\u00a0[latex]\\frac{\\sqrt{77}}{9}[\/latex]<\/p>\n<p>53.\u00a0[latex]-\\frac{\\sqrt{15}}{4}[\/latex]<\/p>\n<p>61.\u00a0[latex]\\sin t=\\frac{1}{2},\\cos t=-\\frac{\\sqrt{3}}{2}[\/latex]<\/p>\n<p>63.\u00a0[latex]\\sin t=-\\frac{\\sqrt{2}}{2},\\cos t=-\\frac{\\sqrt{2}}{2}[\/latex]<\/p>\n<p>65.\u00a0[latex]\\sin t=\\frac{\\sqrt{3}}{2},\\cos t=-\\frac{1}{2}[\/latex]<\/p>\n<p>67.\u00a0[latex]\\sin t=-\\frac{\\sqrt{2}}{2},\\cos t=\\frac{\\sqrt{2}}{2}[\/latex]<\/p>\n<p>69.\u00a0[latex]\\sin t=0,\\cos t=-1[\/latex]<\/p>\n<p>73.\u00a0[latex]\\sin t=\\frac{1}{2},\\cos t=\\frac{\\sqrt{3}}{2}[\/latex]<\/p>\n<p>81.\u00a0\u22120.1736<\/p>\n<p>83.\u00a00.9511<\/p>\n<p>87.\u00a0\u22120.1392<\/p>\n<p>89.\u00a0\u22120.7660<\/p>\n<h1>Other Trigonometric Functions<\/h1>\n<p>7.\u00a0[latex]\\frac{2\\sqrt{3}}{3}[\/latex]<\/p>\n<p>13. 1<\/p>\n<p>19.\u00a0[latex]-\\frac{2\\sqrt{3}}{3}[\/latex]<\/p>\n<p>21.\u00a0[latex]\\sqrt{3}[\/latex]<\/p>\n<p>33.\u00a0[latex]\\frac{\\sqrt{3}}{3}[\/latex]<\/p>\n<p>35.\u00a0\u22122<\/p>\n<p>39.\u00a0If [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]<\/p>\n<p>41.\u00a0[latex]\\sec t=2,\\csc t=\\frac{2\\sqrt{3}}{3},\\tan t=\\sqrt{3},\\cot t=\\frac{\\sqrt{3}}{3}[\/latex]<\/p>\n<p>43.\u00a0[latex]-\\frac{\\sqrt{2}}{2}[\/latex]<\/p>\n<p>45.\u00a03.1<\/p>\n<p>47.\u00a01.4<\/p>\n<p>53.\u00a0\u20130.228<\/p>\n<p>55.\u00a0\u20132.414<\/p>\n<p>57.\u00a01.414<\/p>\n<p>61.\u00a01.556<\/p>\n<p>73.\u00a013.77 hours, period: [latex]1000\\pi[\/latex]<\/p>\n<p>75.\u00a07.73 inches<\/p>\n","protected":false},"author":13,"menu_order":13,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":224,"module-header":"- Select Header 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