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