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Тригонометрическое уравнение sin x = a

Тригонометрическое уравнение sin x = a. Табличные значения sin t и arcsin a. sin t = a, a [-1;1]. t – любое. sin π / 2 = 1. sin (- π / 2 ) = -1. sin π / 3 = √3 / 2. sin (- π / 3 ) = - √3 / 2. sin π / 4 = √2 / 2. sin (- π / 4 ) = - √2 / 2. sin π / 6 = 1 / 2.

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Тригонометрическое уравнение sin x = a

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  1. Тригонометрическоеуравнениеsin x = a

  2. Табличные значения sin t и arcsin a sin t = a, a [-1;1] t – любое sin π/2 = 1 sin (- π/2) = -1 sin π/3 = √3/2 sin (-π/3)= -√3/2 sin π/4 = √2/2 sin (-π/4) = -√2/2 sin π/6 = 1/2 sin (-π/6)= -1/2 sin 0 = 0 arcsin a = t, a  [-1;1] t[-π/2;π/2] arcsin 1 = π/2 arcsin (-1) = -π/2 arcsin √3/2 = π/3 arcsin (-√3/2) = -π/3 arcsin √2/2 = π/4 arcsin (-√2/2) = -π/4 arcsin 1/2 = π/6 arcsin (-1/2) = - π/6 arcsin 0 = 0

  3. Использование формулы arcsin (-a) = – arcsin a arcsin (- ½) = = – arcsin ½ = – π/6 = arcsin 1 = arcsin √3/2 = arcsin √2/2 = arcsin 1/2 = arcsin 0 5 табличных значений arcsin a

  4. Формулa корней тригонометрического уравнения sint =а , где а  [-1;1] или Частные случаи sin t=0 t = πn‚ nЄZ sin t=1 t = π/2 + 2πn‚ nЄZ sin t = -1 t = -π/2+2πn‚ nЄZ Примеры: 1) sin t = - 1/2 t= (-1)k arcsin(-1/2)+πk, k Z t= (-1)k+1π/3+ πk, k Z (-1)k. (-1) = (-1)k+1

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