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TABELA DE IDENTIDADES TRIGONOMÉTRICAS FUNDAMENTAIS sen2x + cos2x = 1 sen2x = 1 – cos2 x cos2x = 1 – sen2x
sen x = √1 − �����
cos x = √1 − ��� sen (-x) = -sen x cos (-x) = cos x sen( x + 2π) = sen x cos(x + 2π) = cos x
tg x = �� ���� �
cotg x = �
�� � = ��� ��� �
sec x = �
��� �
cossec x = �
�� � sec2x = 1 + tg2x cossec2x = 1+cotg2x
cos x = cos2�� - sen
2��
cos x sen y = �� ���� + �� + ��� − ���
cos x sen y = �� ������ + �� + ����� − ���
sen x sen y = �� ������ − �� + ����� + ���
sen αx = �����
��������
�
cos αx = � �����
��������
�
tg αx = �����
�� �����
�
sen3x = 3senx – 4sen3x cos3x = 4cos3x – 3cosx
tg3x = !��� ��"�
� !����
sen�� = ±$� %&� �
�
cos��= ±$��%&� �
�
tg�� = ±$� %&� �
��%&� �
tg x .co tg x = �� ���� � .
��� ��� � = 1
ÂNGULO METADE
sen2x = ����
�� ���� = � %&���
�
cos2x = �
�� ���� = ��%&���
�
ÂNGULO DUPLO sen2x = 2.sen x.cos x cos2x = cos2x – sen2x = 2cos2x – 1
tg2x = ��� �
� ����
LEI DOS SENOS
'� () = +
� ,- = �� .) = 20
LEI DOS COSSENOS a2 = b2 + c2 – 2bc.cosÂ
COSSENO, SENO E TANGENTE DA SOMA E DA DIFERENÇA DE
DOIS ANGULOS Cos(α + β) = cosα.cosβ – senα.cosβ Cos(α - β) = cosα.cosβ + senα.cosβ Sen(α + β) = senα.cosβ + cosα.senβ Sen(α - β) = senα.cosβ - cosα.senβ
tg(α + β) = ��1���2
� ��1.��2
tg(α - β) = ��1 ��2
����1.��2
cotg (α + β) = %&��1.%&��2 �%&��1� %&��2
cotg (α + β) = %&��1.%&��2��%&��1 %&��2