{"id":2244,"date":"2019-05-07T16:33:46","date_gmt":"2019-05-07T16:33:46","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-dutchess-precalculus\/?post_type=chapter&p=2244"},"modified":"2019-05-12T21:10:45","modified_gmt":"2019-05-12T21:10:45","slug":"3-1-exercises","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-dutchess-precalculus\/chapter\/3-1-exercises\/","title":{"raw":"3.1 Section Exercises","rendered":"3.1 Section Exercises"},"content":{"raw":"
\r\n

3.1 Section Exercises<\/h3>\r\nFor Exercises 1-10, find the values of all six trigonometric functions of angles A and B in the right triangle \u25b3 ABC in Figure 8.\r\n\r\n[caption id=\"attachment_1759\" align=\"aligncenter\" width=\"300\"]\"figure Figure 8. A right triangle with angles A B C and sides a b c[\/caption]\r\n
    \r\n \t
  1. $$a = 5$$, $$b = 12$$, $$c = 13$$<\/li>\r\n \t
  2. $$a = 8$$, $$b = 15$$, $$c = 17$$<\/li>\r\n \t
  3. $$a = 7$$, $$b = 24$$, $$c = 25$$<\/li>\r\n \t
  4. $$a = 20$$, $$b = 21$$, $$c = 29$$<\/li>\r\n \t
  5. $$a = 9$$, $$b = 40$$, $$c = 41$$<\/li>\r\n \t
  6. $$a = 1$$, $$b = 2$$, $$c = \\sqrt{5}$$<\/li>\r\n \t
  7. $$a = 1$$, $$b = 3$$<\/li>\r\n \t
  8. $$a = 2$$, $$b = 5$$<\/li>\r\n \t
  9. $$a = 5$$, $$c = 6$$<\/li>\r\n \t
  10. $$b = 7$$, $$c = 8$$<\/li>\r\n<\/ol>\r\nFor Exercises 11-18, find the values of the other five trigonometric functions of the acute angle A given the indicated value of one of the functions.\r\n
      \r\n \t
    1. $$\\sin\\;A = \\frac{3}{4}$$<\/li>\r\n \t
    2. $$\\cos\\;A = \\frac{2}{3}$$<\/li>\r\n \t
    3. $$\\cos\\;A = \\frac{2}{\\sqrt{10}}$$<\/li>\r\n \t
    4. $$\\sin\\;A = \\frac{2}{4}$$<\/li>\r\n \t
    5. $$\\tan\\;A = \\frac{5}{9}$$<\/li>\r\n \t
    6. $$\\tan\\;A = 3$$<\/li>\r\n \t
    7. $$\\sec\\;A = \\frac{7}{3}$$<\/li>\r\n \t
    8. $$\\csc\\;A = 3$$<\/li>\r\n<\/ol>\r\nFor Exercises 19-23, write the given number as a trigonometric function of an acute angle less than 45\u00b0 .\r\n
        \r\n \t
      1. $$\\sin\\;87^\\circ$$<\/li>\r\n \t
      2. $$\\sin\\;53^\\circ$$<\/li>\r\n \t
      3. $$\\cos\\;46^\\circ$$<\/li>\r\n \t
      4. $$\\tan\\;66^\\circ$$<\/li>\r\n \t
      5. $$\\sec\\;77^\\circ$$<\/li>\r\n<\/ol>\r\nFor Exercises 24-28, write the given number as a trigonometric function of an acute angle greater than 45$$^\\circ$$ .\r\n
          \r\n \t
        1. $$\\sin\\;1^\\circ$$<\/li>\r\n \t
        2. $$\\cos\\;13^\\circ$$<\/li>\r\n \t
        3. $$\\tan\\;26^\\circ$$<\/li>\r\n \t
        4. $$\\cot\\;10^\\circ$$<\/li>\r\n \t
        5. $$\\csc\\;43^\\circ$$<\/li>\r\n \t
        6. In Example 1.7 we found the values of all six trigonometric functions of 60\u00b0 and 30\u00b0 .\r\n
            \r\n \t
          1. Does $$\\;\\sin\\;30^\\circ ~+~ \\sin\\;30^\\circ ~=~ \\sin\\;60^\\circ$$?<\/li>\r\n \t
          2. Does $$\\;\\cos\\;30^\\circ ~+~ \\cos\\;30^\\circ ~=~ \\cos\\;60^\\circ$$?<\/li>\r\n \t
          3. Does $$\\;\\tan\\;30^\\circ ~+~ \\tan\\;30^\\circ ~=~ \\tan\\;60^\\circ$$?<\/li>\r\n \t
          4. Does $$\\;2\\,\\sin\\;30^\\circ\\,\\cos\\;30^\\circ ~=~ \\sin\\;60^\\circ$$?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
          5. For an acute angle $$A$$, can $$\\sin\\;A$$ be larger than $$1$$? Explain your answer.<\/li>\r\n \t
          6. For an acute angle $$A$$, can $$\\cos\\;A$$ be larger than $$1$$? Explain your answer.<\/li>\r\n \t
          7. For an acute angle $$A$$, can $$\\sin\\;A$$ be larger than $$\\tan\\;A$$? Explain your answer.<\/li>\r\n \t
          8. If $$A$$ and $$B$$ are acute angles and $$A < B$$, explain why $$\\sin\\;A < \\sin\\;B$$.<\/li>\r\n \t
          9. If $$A$$ and $$B$$ are acute angles and $$A < B$$, explain why $$\\cos\\;A > \\cos\\;B$$.<\/li>\r\n \t
          10. Prove the Cofunction Theorem. Hint: Draw a right triangle and label the angles and sides.<\/em><\/li>\r\n<\/ol>\r\n<\/div>\r\n ","rendered":"
            \n

            3.1 Section Exercises<\/h3>\n

            For Exercises 1-10, find the values of all six trigonometric functions of angles A and B in the right triangle \u25b3 ABC in Figure 8.<\/p>\n

            \"figure<\/p>\n

            Figure 8. A right triangle with angles A B C and sides a b c<\/p>\n<\/div>\n

              \n
            1. $$a = 5$$, $$b = 12$$, $$c = 13$$<\/li>\n
            2. $$a = 8$$, $$b = 15$$, $$c = 17$$<\/li>\n
            3. $$a = 7$$, $$b = 24$$, $$c = 25$$<\/li>\n
            4. $$a = 20$$, $$b = 21$$, $$c = 29$$<\/li>\n
            5. $$a = 9$$, $$b = 40$$, $$c = 41$$<\/li>\n
            6. $$a = 1$$, $$b = 2$$, $$c = \\sqrt{5}$$<\/li>\n
            7. $$a = 1$$, $$b = 3$$<\/li>\n
            8. $$a = 2$$, $$b = 5$$<\/li>\n
            9. $$a = 5$$, $$c = 6$$<\/li>\n
            10. $$b = 7$$, $$c = 8$$<\/li>\n<\/ol>\n

              For Exercises 11-18, find the values of the other five trigonometric functions of the acute angle A given the indicated value of one of the functions.<\/p>\n

                \n
              1. $$\\sin\\;A = \\frac{3}{4}$$<\/li>\n
              2. $$\\cos\\;A = \\frac{2}{3}$$<\/li>\n
              3. $$\\cos\\;A = \\frac{2}{\\sqrt{10}}$$<\/li>\n
              4. $$\\sin\\;A = \\frac{2}{4}$$<\/li>\n
              5. $$\\tan\\;A = \\frac{5}{9}$$<\/li>\n
              6. $$\\tan\\;A = 3$$<\/li>\n
              7. $$\\sec\\;A = \\frac{7}{3}$$<\/li>\n
              8. $$\\csc\\;A = 3$$<\/li>\n<\/ol>\n

                For Exercises 19-23, write the given number as a trigonometric function of an acute angle less than 45\u00b0 .<\/p>\n

                  \n
                1. $$\\sin\\;87^\\circ$$<\/li>\n
                2. $$\\sin\\;53^\\circ$$<\/li>\n
                3. $$\\cos\\;46^\\circ$$<\/li>\n
                4. $$\\tan\\;66^\\circ$$<\/li>\n
                5. $$\\sec\\;77^\\circ$$<\/li>\n<\/ol>\n

                  For Exercises 24-28, write the given number as a trigonometric function of an acute angle greater than 45$$^\\circ$$ .<\/p>\n

                    \n
                  1. $$\\sin\\;1^\\circ$$<\/li>\n
                  2. $$\\cos\\;13^\\circ$$<\/li>\n
                  3. $$\\tan\\;26^\\circ$$<\/li>\n
                  4. $$\\cot\\;10^\\circ$$<\/li>\n
                  5. $$\\csc\\;43^\\circ$$<\/li>\n
                  6. In Example 1.7 we found the values of all six trigonometric functions of 60\u00b0 and 30\u00b0 .\n
                      \n
                    1. Does $$\\;\\sin\\;30^\\circ ~+~ \\sin\\;30^\\circ ~=~ \\sin\\;60^\\circ$$?<\/li>\n
                    2. Does $$\\;\\cos\\;30^\\circ ~+~ \\cos\\;30^\\circ ~=~ \\cos\\;60^\\circ$$?<\/li>\n
                    3. Does $$\\;\\tan\\;30^\\circ ~+~ \\tan\\;30^\\circ ~=~ \\tan\\;60^\\circ$$?<\/li>\n
                    4. Does $$\\;2\\,\\sin\\;30^\\circ\\,\\cos\\;30^\\circ ~=~ \\sin\\;60^\\circ$$?<\/li>\n<\/ol>\n<\/li>\n
                    5. For an acute angle $$A$$, can $$\\sin\\;A$$ be larger than $$1$$? Explain your answer.<\/li>\n
                    6. For an acute angle $$A$$, can $$\\cos\\;A$$ be larger than $$1$$? Explain your answer.<\/li>\n
                    7. For an acute angle $$A$$, can $$\\sin\\;A$$ be larger than $$\\tan\\;A$$? Explain your answer.<\/li>\n
                    8. If $$A$$ and $$B$$ are acute angles and $$A < B$$, explain why $$\\sin\\;A < \\sin\\;B$$.<\/li>\n
                    9. If $$A$$ and $$B$$ are acute angles and $$A < B$$, explain why $$\\cos\\;A > \\cos\\;B$$.<\/li>\n
                    10. Prove the Cofunction Theorem. Hint: Draw a right triangle and label the angles and sides.<\/em><\/li>\n<\/ol>\n<\/div>\n

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