мұндағы -берілген сан.
Қарапайым тригонометриялық теңдеулерді шешу дегеніміз – тригонометриялық функцияның мәні санына тең болатын барлық бұрыштарды табу.
Синус функциясы кесіндісінде өсетінін және -ден -ге дейінгі барлық мәндерді қабылдайтын білеміз. Біз кез келген анықталу облысында жатқан бұрышының синусын, косинусын, тангенсін, котангенсін таба аламыз. Енді кері жағдайды қарастырайық: берілген функцияның мәні бойынша оған сәйкес келетін бұрышты табу керек.
Анықтама. 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)
Достарыңызбен бөлісу: |