Тригонометрия II by Kim https://padlet.com/neah_kimuro/c1x9ds79hb81 Я люблю математику! en-us 2018-06-07 16:35:26 UTC 2023-12-24 16:48:54 UTC hello@padlet.com Тригонометрия II neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151205 2018-06-07 16:36:54 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151205 Положительные и отрицательные углы neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151355 2018-06-07 16:37:30 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151355 Всякий угол можно представить в виде х = α + n × 360°, где 0° ≤ α < 360°, n є Z neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151460 2018-06-07 16:38:02 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151460 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151612 2018-06-07 16:38:42 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151612 Виды углов neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151703 2018-06-07 16:39:05 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151703 Острый: 0° < х < 90° neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151764 2018-06-07 16:39:23 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151764 Тригонометрическая окружность neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151853 2018-06-07 16:39:44 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266151853 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152053 2018-06-07 16:40:29 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152053 Прямой: х = 90° neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152160 2018-06-07 16:40:50 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152160 Тупой: 90° < х < 180° neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152221 2018-06-07 16:41:06 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152221 Развернутый: х = 180° neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152267 2018-06-07 16:41:14 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152267 Углы III-й четверти: 180° < х < 270° neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152298 2018-06-07 16:41:21 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152298 Углы IV-й четверти: 270° < х < 360° neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152346 2018-06-07 16:41:32 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152346 Полный: х = 360° neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152427 2018-06-07 16:41:54 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152427 Опр 1: Окружность, с r равным 1, называется тригонометрической окружностью. neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152666 2018-06-07 16:42:45 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152666 Опр 2: Синусом угла αназывается ордината точки Pα, полученная путем поворота тригонометрического начала на угол α. neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152744 2018-06-07 16:43:03 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152744 Опр 3: Косинусом угла α называется абсцисса точки Pα, полученная путем поворота тригонометрического начала на угол α. neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152793 2018-06-07 16:43:15 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152793 Знаки значений тригонометрических функций по четвертям neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152912 2018-06-07 16:43:37 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266152912 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153041 2018-06-07 16:44:13 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153041 Тригонометрические функции отрицательного угла neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153222
Sin (-α) = - sin α
Cos (-α) = cos α
Tan (-α) = - tan α
Cot (-α) = - cot α]]> 2018-06-07 16:45:05 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153222 Формулы приведения neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153675 Sin (90° – α) = cos α

Cos (90° – α) = sin α

Tan (90° – α) = cot α

Cot (90° – α) = tan α

]]> 2018-06-07 16:47:03 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153675 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153798 Sin (90° + α) = cos α

Cos (90° + α) = - sin α

Tan (90° + α) = - cot α

Cot (90° + α) = - tan α

]]> 2018-06-07 16:47:36 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153798 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153886 Sin (180° – α) = sin α

Cos (180° – α) = - cos α

Tan (180° – α) = - tan α

Cot (180° – α) = - cot α

]]> 2018-06-07 16:47:58 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153886 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153942 Sin (180° + α) = - sin α

Cos (180° + α) =- cos α

Tan (180° + α) = tan α

Cot (180° + α) = cot α

]]> 2018-06-07 16:48:15 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266153942 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154000 Sin (270° – α) = - cos α

Cos (270° – α) = - sin α

Tan (270° – α) = cot α

Cot (270° – α) = tan α

]]> 2018-06-07 16:48:31 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154000 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154081 Sin (270° + α) = - cos α

Cos (270° + α) = sin α

Tan (270° + α) = - cot α

Cot (270° + α) = - tan α

]]> 2018-06-07 16:48:50 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154081 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154143 Sin (360° – α) = - sin α

Cos (360° – α) = cos α

Tan (360° – α) = - tan α

Cot (360° – α) = - cot α

]]> 2018-06-07 16:49:07 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154143 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154191 Sin (360° + α) = sin α

Cos (360° + α) = cos α

Tan (360° + α) = tan α

Cot (360° + α) =cot α

]]> 2018-06-07 16:49:22 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154191 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154245 DEG – градусная мера угла

RAD – радианная мера угла

GRAD – сотенная мера угла

]]> 2018-06-07 16:49:40 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154245 Графики тригонометрических функций neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154312 2018-06-07 16:49:58 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154312 Y = sin x neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154552 X = R

Y = [-1 ; 1]

Xo = { πn, где n є Z}
]]> 2018-06-07 16:51:02 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154552 Y = cos x neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154807 X = R

Y = [-1 ; 1]

Xo =  {π/2+ πn, где n є Z}
]]> 2018-06-07 16:52:14 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266154807 Y = tan x neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266155198 X = R \ { π/2+ πn, где n є Z}

Y = R

Xo = {πn, где n є Z}

]]> 2018-06-07 16:53:58 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266155198 Длинна дуги окружности neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266156738 Площадь сектора

]]> 2018-06-07 17:00:41 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266156738 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266156898 2018-06-07 17:01:29 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266156898 Площадь neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266156993 S = πr2
S = πr2 α /360°
S = r2 x/2]]> 2018-06-07 17:02:02 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266156993 Длина дуги neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157539 L = πrα/(180°)
L = xr]]> 2018-06-07 17:04:43 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157539 Площадь треугольника и параллелограмма neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157687 2018-06-07 17:05:29 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157687 треугольник neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157755 S = 1/2ah ]]> 2018-06-07 17:05:52 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157755 правильный треугольник neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157894 S = (a^2 √3)/4 ]]> 2018-06-07 17:06:15 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157894 высота правильного треугольника neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157977 h = (a√3)/2 ]]> 2018-06-07 17:06:40 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266157977 прямоугольный треугольник neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158078 S = ab/2 ]]> 2018-06-07 17:07:14 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158078 треугольника по синусу neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158177 S = 1/2ab × sin α ]]> 2018-06-07 17:07:39 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158177 параллелограмм neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158261 S = ab × sin α ]]> 2018-06-07 17:08:02 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158261 Формула Герона neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158358 S = √(p(p-a)(p-b)(p-c))]]> 2018-06-07 17:08:23 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158358 Теорема синусов neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158677 В любом треугольнике его стороны противоположны синусам противолежащих углов.]]> 2018-06-07 17:09:41 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158677 a/sin⁡α =b/sin⁡β =c/sin⁡γ neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158775 2018-06-07 17:10:10 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158775 Теорема косинусов neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158875 В любом треугольнике квадрат его стороны равен сумме квадратов двух других сторон, без удвоенного произведения этих сторон на косинус угла между ними.

]]> 2018-06-07 17:10:31 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266158875 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266159685 a2 = b2 + c2 - 2bc × cos ⁡α]]> 2018-06-07 17:14:07 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266159685 neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266159740 cos⁡ α=(b2 + c2 - a2)/2bc]]> 2018-06-07 17:14:20 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266159740 Синус, косинус и тангенс суммы и разности двух углов neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266160485 2018-06-07 17:18:20 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266160485 Синус neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266160700 sin⁡(α+β)=sin⁡ α×cos⁡ β+sin⁡ β×cos α
sin⁡(α-β)=sin ⁡α×cos⁡ β-sin⁡ β×cos α 

]]> 2018-06-07 17:19:30 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266160700 Косинус neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266161113 cos(α+β)=cos⁡ α×cos ⁡β-sin ⁡β×sin⁡ α 
cos⁡(α-β)=cos⁡ α×cos β+sin⁡ β×sin⁡ α ]]> 2018-06-07 17:21:14 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266161113 Тангенс neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266161368 tan⁡(α+β)=tan⁡ α+tan⁡ β /(1-tan β×tan⁡ α )
tan⁡(α-β)=tan α-tan⁡ β /(1+tan β×tan⁡ α )]]> 2018-06-07 17:22:17 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266161368 Основные тригонометрические тождества neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266397861 2018-06-09 08:57:03 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266397861 Формулы двойного угла neah_kimuro https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266690253 2018-06-11 20:18:26 UTC https://padlet.com/neah_kimuro/c1x9ds79hb81/wish/266690253