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ФОРМУЛЫ КОРНЕЙ ТРИГОНОМЕТРИЧЕСКИХ УРАВНЕНИЙ

ФОРМУЛЫ КОРНЕЙ ТРИГОНОМЕТРИЧЕСКИХ УРАВНЕНИЙ. sin x = a. a) x = ± arcsin a + П k, k Z b) x = (–1) k arcsin a + П k, k Z c) x = ± arcsin a + 2 П k, k Z d) x = (–1) k arcsin a + 2 П k, k Z. sin x = a. a) x = ± arcsin a + П k, k Z

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ФОРМУЛЫ КОРНЕЙ ТРИГОНОМЕТРИЧЕСКИХ УРАВНЕНИЙ

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  1. ФОРМУЛЫ КОРНЕЙ ТРИГОНОМЕТРИЧЕСКИХ УРАВНЕНИЙ

  2. sin x = a • a)x = ± arcsin a + Пk, k Z b) x = (–1)k arcsin a + Пk, k Z c) x = ± arcsin a + 2Пk, k Z d) x = (–1)k arcsin a + 2Пk, k Z

  3. sin x = a • a)x = ± arcsin a + Пk, k Z b) x = (–1)k arcsin a + Пk, k Z c) x = ± arcsin a + 2Пk, k Z d) x = (–1)k arcsin a + 2Пk, k Z

  4. cos x = a • a)x = ± arccos a + Пk, k Z b) x = (–1)k arccos a + Пk, k Z c) x = ± arccos a + 2Пk, k Z d) x = (–1)k arccos a + 2Пk, k Z

  5. cos x = a • a)x = ± arccos a + Пk, k Z b) x = (–1)k arccos a + Пk, k Z c) x = ± arccos a + 2Пk, k Z d) x = (–1)k arccos a + 2Пk, k Z

  6. cos x = • x = (–1)k + Пk, k Z • x = ± + Пk, k Z • x = ± + 2Пk, k Z • x = ± + 2Пk, k Z

  7. cos x = • x = (–1)k + Пk, k Z • x = ± + Пk, k Z • x = ± + 2Пk, k Z • x = ± + 2Пk, k Z

  8. sin x = – x = (–1)k+1 + Пk, k Z x = ± + Пk, k Z x = (–1)k+1+ 2Пk, k Z x = (–1)k+1+ Пk, k Z

  9. sin x = – x = (–1)k+1 + Пk, k Z x = ± + Пk, k Z x = (–1)k+1+ 2Пk, k Z x = (–1)k+1+ Пk, k Z

  10. sin x – 1 = 0 x = (–1)k + Пk, k Z x =П+ Пk, k Z x = (–1)k+1+ Пk, k Z x = + Пk, k Z

  11. sin x – 1 = 0 x = (–1)k + Пk, k Z x =П+ Пk, k Z x = (–1)k+1+ Пk, k Z x = + 2Пk, k Z

  12. соs x= 0 x = (–1)k + 2Пk, k Z x =П+ Пk, k Z x = (–1)k+ Пk, k Z x = + Пk, k Z

  13. соs x= 0 x = (–1)k + 2Пk, k Z x =П+ Пk, k Z x = (–1)k+ Пk, k Z x = + Пk, k Z

  14. tg x= 1 x = (–1)k + Пk, k Z x =+ Пk, k Z x = + Пk, k Z x = + 2Пk, k Z

  15. tg x= 1 x = (–1)k + Пk, k Z x =+ Пk, k Z x = + Пk, k Z x = + 2Пk, k Z

  16. tg x=– 3 x = – + Пk, k Z x =arctg 3+ Пk, k Z x = – arctg 3+ Пk, k Z x = – arctg 3+ 2Пk, k Z

  17. tg x=– 3 x = – + Пk, k Z x =arctg 3+ Пk, k Z x = – arctg 3+ Пk, k Z x = – arctg 3+ 2Пk, k Z

  18. ctg x=– x = – + Пk, k Z x = –+ Пk, k Z x = + Пk, k Z x = + 2Пk, k Z

  19. ctg x=– x = – + Пk, k Z x = –+ Пk, k Z x = + Пk, k Z x = + 2Пk, k Z

  20. ДОМАШНЯЯ РАБОТА 2sinx + 1 = 0, xЄ[0; 2π]. cos(2π – x) + sin(π/2 + x) = √2. (sinx + cosx)2 = 1 + sinxcosx, xЄ[0; 2π]. sin(π/2 – x) = sin(– π/4). 4cos2x – 1 = 0. sin2x – 6 sinx = 0. tgx + √3 = 0, xЄ[–2π; 0]. (sinx – 1)(tgx + 1) = 0. 2 sin2x – sinx – 1 = 0. 2 sinx + 3 cosx = 0. cos2x – 3sinxcosx + 1 = 0

  21. 2cosx – 1 = 0, xЄ[0; 2π]. 2cos(π/4 – 3x) = √2. sin3xcosx – sinxcos3x = √3/2. sin(π/2 – x) = sin(– π/4). 2cos2x + sinx + 1 = 0. 4sin2x – sin2x = 3. 2tg2x – 9tgx – 5 = 0. (sinx + 1)(tgx + √3) = 0. cos5x – cos3x = 0.

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