Formulario identidades trigonometricas

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Formulario identidades trigonometricas

Formulario identidades trigonometricas

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  • 1. FUNCIONES TRIGONOMÉTRICAS DE UN NÚMERO REAL (1) ysen =θ (2) x=θcos (3) x y =θtan 0≠x (4) y 1 csc =θ 0≠y (5) x 1 sec =θ 0≠x (6) y x =θcot 0≠y DE UN ÁNGULO EN GENERAL (7) r b sen =θ (8) r a =θcos (9) a b =θtan 0≠a (10) b r =θcsc 0≠b (11) a r =θsec 0≠a (12) b a =θcot 0≠b ESCUELA POLITÉCNICA DEL EJÉRCITO EXTENSIÓN LATACUNGA FORMACIÓN ACADÉMICA – GUÍA DE TRABAJO GEOMETRÍA Y TRIGONOMETRÍA RESUMEN DE FÓRMULAS TRIGONOMÉTRICAS Círculo Trigonométrico r = 1 θ a b r Triángulo Rectángulo Ing. Iván Collantes Vásconez - DOCENTE
  • 2. IDENTIDADES TRIGONOMÉTRICAS IDENTIDADES FUNDAMENTALES (13) θ θ θ cos tan sen = (14) θ θ θ sen cos cot = (15) θ θ tan 1 cot = (16) θ θ sen 1 csc = (17) θ θ cos 1 sec = (18) 1cos22 =+ θθsen (19) θθ 22 sec1tan =+ (20) θθ 22 csccot1 =+ FÓRMULAS DE SUMA Y RESTA (21) ysenxyxsenyxsen coscos)( +=+ (22) ysenxyxsenyxsen coscos)( −=− (23) ysenxsenyxyx −=+ coscos)cos( (24) ysenxsenyxyx +=− coscos)cos( (25) yx yx yx tantan1 tantan )tan( − + =+ (26) yx yx yx tantan1 tantan )tan( + − =− FÓRMULAS PARA ÁNGULO DOBLE FÓRMULAS PARA ÁNGULO MITAD (27) θθθ cos22 sensen = (32) 2 cos1 2 θθ − =sen (28) θθθ 22 cos2cos sen−= (33) 2 cos1 2 cos θθ + = (29) 1cos22cos 2 −= θθ (34) θ θθ cos1 cos1 2 tan + − = (30) θθ 2 212cos sen−= (31) θ θ θ 2 tan1 tan2 2tan − = FÓRMULAS PRODUCTO A SUMA FÓRMULAS SUMA A PRODUCTO (35) )]cos()[cos( 2 1 yxyxsenysenx +−−= (38) 2 cos 2 2 yxyx sensenysenx −+ =+ (36) )]cos()[cos( 2 1 coscos yxyxyx ++−= (39) 2 cos 2 2 yxyx sensenysenx +− =− (37) )]()([ 2 1 cos yxsenyxsenysenx −++= (40) 2 cos 2 cos2coscos yxyx yx −+ =+ (41) 22 2coscos yx sen yx senyx −+ −=−