{
    "nazvanie": "Точные значения синуса и косинуса для углов, кратных 3 градусам",
    "istochnik": "https://scolaire.ru/tochnye-znacheniya-sinusa-kosinusa.php",
    "izdatel": "Школяр",
    "licenziya": "https://creativecommons.org/licenses/by/4.0/deed.ru",
    "usloviye": "Использование разрешено при указании источника: Школяр, https://scolaire.ru/tochnye-znacheniya-sinusa-kosinusa.php",
    "svereno": "2026-08-15",
    "o_proverke": "Каждое из 60 выражений сверено с эталонным значением на 55 знаках после запятой. Не сошлось ни одного.",
    "stroki": [
        {
            "ugol_gradusov": 3,
            "sin_tochno_tex": "\\frac{- \\sqrt{6} \\sqrt{2 \\sqrt{5} + 10} - \\sqrt{6} - \\sqrt{2} + \\sqrt{10} + \\sqrt{2} \\sqrt{2 \\sqrt{5} + 10} + \\sqrt{30}}{16}",
            "cos_tochno_tex": "\\frac{- \\sqrt{10} - \\sqrt{6} + \\sqrt{2} + \\sqrt{2} \\sqrt{2 \\sqrt{5} + 10} + \\sqrt{30} + \\sqrt{6} \\sqrt{2 \\sqrt{5} + 10}}{16}",
            "sin_30_znakov": "0.0523359562429438327221186296091",
            "cos_30_znakov": "0.998629534754573873784492058439",
            "stepen_min_mnogochlena": 16
        },
        {
            "ugol_gradusov": 6,
            "sin_tochno_tex": "\\frac{- \\sqrt{5} - 1 + \\sqrt{6} \\sqrt{5 - \\sqrt{5}}}{8}",
            "cos_tochno_tex": "\\frac{\\sqrt{3} + \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{15}}{8}",
            "sin_30_znakov": "0.104528463267653471399834154803",
            "cos_30_znakov": "0.994521895368273336922691944981",
            "stepen_min_mnogochlena": 8
        },
        {
            "ugol_gradusov": 9,
            "sin_tochno_tex": "\\frac{- 2 \\sqrt{5 - \\sqrt{5}} + \\sqrt{2} + \\sqrt{10}}{8}",
            "cos_tochno_tex": "\\frac{\\sqrt{2} + \\sqrt{10} + 2 \\sqrt{5 - \\sqrt{5}}}{8}",
            "sin_30_znakov": "0.156434465040230869010105319467",
            "cos_30_znakov": "0.987688340595137726190040247693",
            "stepen_min_mnogochlena": 8
        },
        {
            "ugol_gradusov": 12,
            "sin_tochno_tex": "\\frac{- \\sqrt{15} + \\sqrt{3} + \\sqrt{2 \\sqrt{5} + 10}}{8}",
            "cos_tochno_tex": "\\frac{-1 + \\sqrt{5} + \\sqrt{6} \\sqrt{\\sqrt{5} + 5}}{8}",
            "sin_30_znakov": "0.207911690817759337101742284405",
            "cos_30_znakov": "0.978147600733805637928566747870",
            "stepen_min_mnogochlena": 4
        },
        {
            "ugol_gradusov": 15,
            "sin_tochno_tex": "\\frac{- \\sqrt{2} + \\sqrt{6}}{4}",
            "cos_tochno_tex": "\\frac{\\sqrt{2} + \\sqrt{6}}{4}",
            "sin_30_znakov": "0.258819045102520762348898837624",
            "cos_30_znakov": "0.965925826289068286749743199729",
            "stepen_min_mnogochlena": 4
        },
        {
            "ugol_gradusov": 18,
            "sin_tochno_tex": "\\frac{-1 + \\sqrt{5}}{4}",
            "cos_tochno_tex": "\\frac{\\sqrt{2 \\sqrt{5} + 10}}{4}",
            "sin_30_znakov": "0.309016994374947424102293417183",
            "cos_30_znakov": "0.951056516295153572116439333379",
            "stepen_min_mnogochlena": 4
        },
        {
            "ugol_gradusov": 21,
            "sin_tochno_tex": "\\frac{- \\sqrt{30} - \\sqrt{6} + \\sqrt{2} + \\sqrt{10} + \\sqrt{2} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{6} \\sqrt{10 - 2 \\sqrt{5}}}{16}",
            "cos_tochno_tex": "\\frac{- \\sqrt{2} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{2} + \\sqrt{6} + \\sqrt{10} + \\sqrt{30} + \\sqrt{6} \\sqrt{10 - 2 \\sqrt{5}}}{16}",
            "sin_30_znakov": "0.358367949545300273484137789413",
            "cos_30_znakov": "0.933580426497201748990043063140",
            "stepen_min_mnogochlena": 16
        },
        {
            "ugol_gradusov": 24,
            "sin_tochno_tex": "\\frac{- \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{3} + \\sqrt{15}}{8}",
            "cos_tochno_tex": "\\frac{1 + \\sqrt{5} + \\sqrt{6} \\sqrt{5 - \\sqrt{5}}}{8}",
            "sin_30_znakov": "0.406736643075800207753985990342",
            "cos_30_znakov": "0.913545457642600895502127571985",
            "stepen_min_mnogochlena": 4
        },
        {
            "ugol_gradusov": 27,
            "sin_tochno_tex": "\\frac{- \\sqrt{10} + \\sqrt{2} + 2 \\sqrt{\\sqrt{5} + 5}}{8}",
            "cos_tochno_tex": "\\frac{- \\sqrt{2} + \\sqrt{10} + 2 \\sqrt{\\sqrt{5} + 5}}{8}",
            "sin_30_znakov": "0.453990499739546791560408366358",
            "cos_30_znakov": "0.891006524188367862359709571414",
            "stepen_min_mnogochlena": 8
        },
        {
            "ugol_gradusov": 30,
            "sin_tochno_tex": "\\frac{1}{2}",
            "cos_tochno_tex": "\\frac{\\sqrt{3}}{2}",
            "sin_30_znakov": "0.500000000000000000000000000000",
            "cos_30_znakov": "0.866025403784438646763723170753",
            "stepen_min_mnogochlena": 2
        },
        {
            "ugol_gradusov": 33,
            "sin_tochno_tex": "\\frac{- \\sqrt{2} \\sqrt{2 \\sqrt{5} + 10} - \\sqrt{6} - \\sqrt{2} + \\sqrt{10} + \\sqrt{30} + \\sqrt{6} \\sqrt{2 \\sqrt{5} + 10}}{16}",
            "cos_tochno_tex": "\\frac{- \\sqrt{30} - \\sqrt{2} + \\sqrt{6} + \\sqrt{10} + \\sqrt{2} \\sqrt{2 \\sqrt{5} + 10} + \\sqrt{6} \\sqrt{2 \\sqrt{5} + 10}}{16}",
            "sin_30_znakov": "0.544639035015027082224083692082",
            "cos_30_znakov": "0.838670567945424029637590941805",
            "stepen_min_mnogochlena": 16
        },
        {
            "ugol_gradusov": 36,
            "sin_tochno_tex": "\\frac{\\sqrt{10 - 2 \\sqrt{5}}}{4}",
            "cos_tochno_tex": "\\frac{1 + \\sqrt{5}}{4}",
            "sin_30_znakov": "0.587785252292473129168705954639",
            "cos_30_znakov": "0.809016994374947424102293417183",
            "stepen_min_mnogochlena": 2
        },
        {
            "ugol_gradusov": 39,
            "sin_tochno_tex": "\\frac{- \\sqrt{6} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{2} + \\sqrt{6} + \\sqrt{10} + \\sqrt{2} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{30}}{16}",
            "cos_tochno_tex": "\\frac{- \\sqrt{10} - \\sqrt{2} + \\sqrt{6} + \\sqrt{2} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{30} + \\sqrt{6} \\sqrt{10 - 2 \\sqrt{5}}}{16}",
            "sin_30_znakov": "0.629320391049837452705902458280",
            "cos_30_znakov": "0.777145961456970879979937743672",
            "stepen_min_mnogochlena": 16
        },
        {
            "ugol_gradusov": 42,
            "sin_tochno_tex": "- \\frac{- \\sqrt{6} \\sqrt{\\sqrt{5} + 5} - 1 + \\sqrt{5}}{8}",
            "cos_tochno_tex": "\\frac{- \\sqrt{3} + \\sqrt{2 \\sqrt{5} + 10} + \\sqrt{15}}{8}",
            "sin_30_znakov": "0.669130606358858213826273330687",
            "cos_30_znakov": "0.743144825477394235014697048974",
            "stepen_min_mnogochlena": 8
        },
        {
            "ugol_gradusov": 45,
            "sin_tochno_tex": "\\frac{\\sqrt{2}}{2}",
            "cos_tochno_tex": "\\frac{\\sqrt{2}}{2}",
            "sin_30_znakov": "0.707106781186547524400844362105",
            "cos_30_znakov": "0.707106781186547524400844362105",
            "stepen_min_mnogochlena": 2
        },
        {
            "ugol_gradusov": 48,
            "sin_tochno_tex": "\\frac{- \\sqrt{3} + \\sqrt{2 \\sqrt{5} + 10} + \\sqrt{15}}{8}",
            "cos_tochno_tex": "- \\frac{- \\sqrt{6} \\sqrt{\\sqrt{5} + 5} - 1 + \\sqrt{5}}{8}",
            "sin_30_znakov": "0.743144825477394235014697048974",
            "cos_30_znakov": "0.669130606358858213826273330687",
            "stepen_min_mnogochlena": 4
        },
        {
            "ugol_gradusov": 51,
            "sin_tochno_tex": "\\frac{- \\sqrt{10} - \\sqrt{2} + \\sqrt{6} + \\sqrt{2} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{30} + \\sqrt{6} \\sqrt{10 - 2 \\sqrt{5}}}{16}",
            "cos_tochno_tex": "\\frac{- \\sqrt{6} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{2} + \\sqrt{6} + \\sqrt{10} + \\sqrt{2} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{30}}{16}",
            "sin_30_znakov": "0.777145961456970879979937743672",
            "cos_30_znakov": "0.629320391049837452705902458280",
            "stepen_min_mnogochlena": 16
        },
        {
            "ugol_gradusov": 54,
            "sin_tochno_tex": "\\frac{1 + \\sqrt{5}}{4}",
            "cos_tochno_tex": "\\frac{\\sqrt{10 - 2 \\sqrt{5}}}{4}",
            "sin_30_znakov": "0.809016994374947424102293417183",
            "cos_30_znakov": "0.587785252292473129168705954639",
            "stepen_min_mnogochlena": 4
        },
        {
            "ugol_gradusov": 57,
            "sin_tochno_tex": "\\frac{- \\sqrt{30} - \\sqrt{2} + \\sqrt{6} + \\sqrt{10} + \\sqrt{2} \\sqrt{2 \\sqrt{5} + 10} + \\sqrt{6} \\sqrt{2 \\sqrt{5} + 10}}{16}",
            "cos_tochno_tex": "\\frac{- \\sqrt{2} \\sqrt{2 \\sqrt{5} + 10} - \\sqrt{6} - \\sqrt{2} + \\sqrt{10} + \\sqrt{30} + \\sqrt{6} \\sqrt{2 \\sqrt{5} + 10}}{16}",
            "sin_30_znakov": "0.838670567945424029637590941805",
            "cos_30_znakov": "0.544639035015027082224083692082",
            "stepen_min_mnogochlena": 16
        },
        {
            "ugol_gradusov": 60,
            "sin_tochno_tex": "\\frac{\\sqrt{3}}{2}",
            "cos_tochno_tex": "\\frac{1}{2}",
            "sin_30_znakov": "0.866025403784438646763723170753",
            "cos_30_znakov": "0.500000000000000000000000000000",
            "stepen_min_mnogochlena": 1
        },
        {
            "ugol_gradusov": 63,
            "sin_tochno_tex": "\\frac{- \\sqrt{2} + \\sqrt{10} + 2 \\sqrt{\\sqrt{5} + 5}}{8}",
            "cos_tochno_tex": "\\frac{- \\sqrt{10} + \\sqrt{2} + 2 \\sqrt{\\sqrt{5} + 5}}{8}",
            "sin_30_znakov": "0.891006524188367862359709571414",
            "cos_30_znakov": "0.453990499739546791560408366358",
            "stepen_min_mnogochlena": 8
        },
        {
            "ugol_gradusov": 66,
            "sin_tochno_tex": "\\frac{1 + \\sqrt{5} + \\sqrt{6} \\sqrt{5 - \\sqrt{5}}}{8}",
            "cos_tochno_tex": "\\frac{- \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{3} + \\sqrt{15}}{8}",
            "sin_30_znakov": "0.913545457642600895502127571985",
            "cos_30_znakov": "0.406736643075800207753985990342",
            "stepen_min_mnogochlena": 8
        },
        {
            "ugol_gradusov": 69,
            "sin_tochno_tex": "\\frac{- \\sqrt{2} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{2} + \\sqrt{6} + \\sqrt{10} + \\sqrt{30} + \\sqrt{6} \\sqrt{10 - 2 \\sqrt{5}}}{16}",
            "cos_tochno_tex": "\\frac{- \\sqrt{30} - \\sqrt{6} + \\sqrt{2} + \\sqrt{10} + \\sqrt{2} \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{6} \\sqrt{10 - 2 \\sqrt{5}}}{16}",
            "sin_30_znakov": "0.933580426497201748990043063140",
            "cos_30_znakov": "0.358367949545300273484137789413",
            "stepen_min_mnogochlena": 16
        },
        {
            "ugol_gradusov": 72,
            "sin_tochno_tex": "\\frac{\\sqrt{2 \\sqrt{5} + 10}}{4}",
            "cos_tochno_tex": "\\frac{-1 + \\sqrt{5}}{4}",
            "sin_30_znakov": "0.951056516295153572116439333379",
            "cos_30_znakov": "0.309016994374947424102293417183",
            "stepen_min_mnogochlena": 2
        },
        {
            "ugol_gradusov": 75,
            "sin_tochno_tex": "\\frac{\\sqrt{2} + \\sqrt{6}}{4}",
            "cos_tochno_tex": "\\frac{- \\sqrt{2} + \\sqrt{6}}{4}",
            "sin_30_znakov": "0.965925826289068286749743199729",
            "cos_30_znakov": "0.258819045102520762348898837624",
            "stepen_min_mnogochlena": 4
        },
        {
            "ugol_gradusov": 78,
            "sin_tochno_tex": "\\frac{-1 + \\sqrt{5} + \\sqrt{6} \\sqrt{\\sqrt{5} + 5}}{8}",
            "cos_tochno_tex": "\\frac{- \\sqrt{15} + \\sqrt{3} + \\sqrt{2 \\sqrt{5} + 10}}{8}",
            "sin_30_znakov": "0.978147600733805637928566747870",
            "cos_30_znakov": "0.207911690817759337101742284405",
            "stepen_min_mnogochlena": 8
        },
        {
            "ugol_gradusov": 81,
            "sin_tochno_tex": "\\frac{\\sqrt{2} + \\sqrt{10} + 2 \\sqrt{5 - \\sqrt{5}}}{8}",
            "cos_tochno_tex": "\\frac{- 2 \\sqrt{5 - \\sqrt{5}} + \\sqrt{2} + \\sqrt{10}}{8}",
            "sin_30_znakov": "0.987688340595137726190040247693",
            "cos_30_znakov": "0.156434465040230869010105319467",
            "stepen_min_mnogochlena": 8
        },
        {
            "ugol_gradusov": 84,
            "sin_tochno_tex": "\\frac{\\sqrt{3} + \\sqrt{10 - 2 \\sqrt{5}} + \\sqrt{15}}{8}",
            "cos_tochno_tex": "\\frac{- \\sqrt{5} - 1 + \\sqrt{6} \\sqrt{5 - \\sqrt{5}}}{8}",
            "sin_30_znakov": "0.994521895368273336922691944981",
            "cos_30_znakov": "0.104528463267653471399834154803",
            "stepen_min_mnogochlena": 4
        },
        {
            "ugol_gradusov": 87,
            "sin_tochno_tex": "\\frac{- \\sqrt{10} - \\sqrt{6} + \\sqrt{2} + \\sqrt{2} \\sqrt{2 \\sqrt{5} + 10} + \\sqrt{30} + \\sqrt{6} \\sqrt{2 \\sqrt{5} + 10}}{16}",
            "cos_tochno_tex": "\\frac{- \\sqrt{6} \\sqrt{2 \\sqrt{5} + 10} - \\sqrt{6} - \\sqrt{2} + \\sqrt{10} + \\sqrt{2} \\sqrt{2 \\sqrt{5} + 10} + \\sqrt{30}}{16}",
            "sin_30_znakov": "0.998629534754573873784492058439",
            "cos_30_znakov": "0.0523359562429438327221186296091",
            "stepen_min_mnogochlena": 16
        },
        {
            "ugol_gradusov": 90,
            "sin_tochno_tex": "1",
            "cos_tochno_tex": "0",
            "sin_30_znakov": "1.00000000000000000000000000000",
            "cos_30_znakov": "0",
            "stepen_min_mnogochlena": 1
        }
    ]
}