Ecuatii Trigonometrice Fundamentale [PDF]

Zitiervorschau

Ecuatii trigonometrice fundamentale � S  f , daca a > 1 � a �( -�, -1) U ( 1, �) � I) sin x  a , a  R. ; Solutia: � k S  ( -1) arcsin a + kp / k �Z } , daca a �[ -1,1] � � Cazuri particulare 1. sin x  0 � x �{ kp , k �Z } � �p 2. sin x  1 � x �� + 2kp , k �Z � �2 � � �p - + 2kp , k �Z � 3. sin x  -1 � x �� �2 � S  f , daca b �( -�, -1) U ( 1, �) � � � II) cos x  b , b  R ; Solutia: � � �arccos b + 2kp / k �Z �dacab �[ -1,1] �S  � � � � � �p Cazuri particulare 1. cos x  0 � x �� + kp , k �Z � �2 � 2. cos x  1 � x �{ 2kp , k �Z }

{

{

3. cos x  -1 � x � p + 2kp , k �Z

III)

tg x  c, c �R

; Solutia:

S  { arctg c + kp / k �Z

}

}

Cazuri particulare 1. tg x  0 � x �{ kp , k �Z } �p � 2. tg x  1 � x �� + kp , k �Z � � �4 � �p - + kp , k �Z � 3. tg x  -1 � x �� �4 � IV) ctg x  d , d �R ; Solutia: S  { arcctg d + kp / k �Z } � �p Cazuri particulare 1. ctg x  0 � x �� + kp , k �Z � �2 � � �p 2. ctg x  1 � x �� + kp , k �Z � �4 � �p � - + kp , k �Z � 3. ctg x  -1 � x �� � �4