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Repeats every 360 o

Y = Sin q. Repeats every 360 o. 2 solutions every 360 o. Y = Cos q. Repeats every 360 o. 2 solutions every 360 o. Y = Tan q. Repeats every 180 o. 1 solution every 180 o. All. Sin. Tan. Cos. Y = Sin 3 q. There are 6 solutions except for when sin 3 q = 1 or -1. Cos 3 q = 0.5602.

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Repeats every 360 o

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  1. Y = Sin q Repeats every 360o 2 solutions every 360o

  2. Y = Cos q Repeats every 360o 2 solutions every 360o

  3. Y = Tan q Repeats every 180o 1 solution every 180o

  4. All Sin Tan Cos

  5. Y = Sin 3q There are 6 solutions except for when sin 3q = 1 or -1

  6. Cos 3q = 0.5602 For 0oq 360o 3q = 55.9o and360 - 55.9o 3q = 55.9o and304.1o But what about second time round or third? so 3q = 55.9o and304.1o or 55.9+360o and 304.1+360o or 55.9+720o and 304.1+720o so 3q = 55.9o and304.1o or 415.9o and 664.1o or 775.9o and 1024.1o q = 18.6o,101.4o, 138.6o, 221.4o, 258.6o, 341.4o

  7. Sin (3q-25o) = 0.234 For 0oq 360o 3q-25o = 13.5o and180 - 13.5o 3q-25o = 13.5o and166.5o But what about second time round or third? so 3q-25o = 13.5o and166.5o or 13.5+360o and 166.5+360o or 13.5+720o and 166.5+720o 3q-25 = 13.5o and166.5o or 373.5o and 526.5o or 733.5o and 886.5o 3q = 38.5o,191.5o, 398.5o, 551.5o, 758.5o, 911.5o q = 12.8o,63.8o, 132.8o, 183.8o, 252.8o, 308.8o

  8. Sin (3q+25o) = 0.234 For 0oq 360o so 3q+25o = 13.5o,166.5o,or 13.5 + 360o, 166.5 + 360o, 13.5 + 720o, 166.5 +720o 3q = -11.5o and168.5o or 348.5o and 528.5o or 708.5o and 888.5o But one of the answers is negative so find the next solution going round a fourth time 3q = -11.5 + 1080o =1068.5 3q = 168.5o,348.5o, 528.5o, 708.5o, 888.5o, 1068.5o q = 56.2o,116.2o, 176.2o, 236.2o, 296.2o, 356.2o

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