• Yarim burchak formulalari: darajalarni tushirish formulalari: . 1.
    		•

    -Mavzu: Keltirish formulalari




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    To\'garak. 10-11

    18-Mavzu: Keltirish formulalari.

    Trigonometrik funksiyalar yig'indisini va ayirmasini ko'paytmaga ke1tirish formulalari



    Endi ikki argument kosinuslarining ko'paytmasini yig'indiga keltirish formulalarini ko’rib chiqamiz:

    Agar bo'lsa, u holda quyidagi formulalar hosil bo’ladi:


    Yarim burchak formulalari:


    darajalarni tushirish formulalari:
    .
    1. Ayniyatlarni isbot qiling:
    1) sin2x - sin2cos2x - cos4x = 1 - 2cos2x; 2) cos2x + sin2x cos4x - sin6x - 1 - 2sin4x;
    3) 6(sin4x + cos4x) - 4(cos6x + sin6x) = 2.
    2. Ifodalarni soddalashtiring:

    1. 2cos(π + x) + 3cos(-x) + cos{π - x); 2) sin(π + x) - 2sin(π - x) - 3sin(-x);

    1. 4cos(-x) + 5sin(π + x) - 2sin(π - x) - 6cos(π + x).

    3. Quyidagi funksiyalarni juft-toqlikka tekshiring:
    1) sin9x; 2) cos9x; 3) sin8x;
    4) 5cos5x + 6cos4x; 5) 3sin3x-2sin2x; 6) 3sin3x + 4cos5x.
    4. Sinus va kosinus funksiyalar qaysi choraklarda bir xil ishoraga ega?
    5. Ayirmalarning ishoralarini aniqlang:
    1) sin38° - sin40°; 2) cos51° - sos21°; 3)sin48° - sin52°;
    4) sinl32D-sinl52°; 5) sinl2° -cos732°.

    1. cosa = -0,5, 90° < a < 180° bo'lsa, sina, tga va ctga ni toping.

    2. Ifodalarni soddalashtiring:

    1) ctg2a - cos2a + cos2actg2a; 2) cos2a + sin2atg2a - tg2a;
    7. Barcha trigonometrik funksiyalarni
    1) sina; 2) cosa; 3) tga; 4) ctga orqali ifodalang.
    8.Agar cosx = -0,8; siny = 0,4; bo'lsa,quyidagilarni toping:
    1) cos(x +y); 2) cos(x-y); 3) sin(x + >0; 4) sin(x-y).

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