Transcription of TRIGONOMETRIC IDENTITIES Reciprocal identities Power ...
1 C 2012 Math Medics LLC. All rights IDENTITIES Reciprocal identitiessinu=1cscucosu=1secutanu=1cotu cotu=1tanucscu=1sinusecu=1cosu Pythagorean Identitiessin2u+ cos2u= 11 + tan2u= sec2u1 + cot2u= csc2u Quotient Identitiestanu=sinucosucotu=cosusinu Co-Function Identitiessin( 2 u) = cosucos( 2 u) = sinutan( 2 u) = cotucot( 2 u) = tanucsc( 2 u) = secusec( 2 u) = cscu Parity IDENTITIES (Even & Odd)sin( u) = sinucos( u) = cosutan( u) = tanucot( u) = cotucsc( u) = cscusec( u) = secu Sum & Difference Formulassin(u v) = sinucosv cosusinvcos(u v) = cosucosv sinusinvtan(u v) =tanu tanv1 tanutanv Double Angle Formulassin(2u) = 2 sinucosucos(2u) = cos2u sin2u= 2 cos2u 1= 1 2 sin2utan(2u) =2 tanu1 tan2u Power - reducing /Half Angle For-mulassin2u=1 cos(2u)2cos2u=1 + cos(2u)2tan2u=1 cos(2u)1 + cos(2u) Sum-to-Product Formulassinu+ sinv= 2 sin(u+v2)cos(u v2)sinu sinv= 2 cos(u+v2)sin(u v2)cosu+ cosv= 2 cos(u+v2)cos(u v2)cosu cosv= 2 sin(u+v2)sin(u v2) Product-to-Sum Formulassinusinv=12[cos(u v) cos(u+v)]
2 ]cosucosv=12[cos(u v) + cos(u+v)]sinucosv=12[sin(u+v) + sin(u v)]cosusinv=12[sin(u+v) sin(u v)
