Tigonometic Identities & Fomulas Tutoial Sevices Mission del Paso Campus Recipocal Identities csc csc Ratio o Quotient Identities cos cot cos cos sec sec cos = cos cos = cot cot cot Pthagoean Identities Pthagoean Identities in Radical Fom cos cos sec cot csc sec Note: thee ae onl thee, basic Pthagoean identities, the othe foms cos ae the same thee identities, just aanged in a diffeent ode. Confunction Identities sec Odd-Even Identities lso called negative angle identities cos cos Sin (-) = - Csc (-) = -csc Cos (-) = cos Sec (-) = sec cot cot Tan (-) = - Cot (-) = -cot csc csc sec Phase Shift = c b Peiod = b Sum and Diffeence Fomulas/Identities How to Find Refeence ngles ( u ucosv cosuv Step : Detemine which quadant the angle is in ( u ucosv cosuv Step : Use the appopiate fomula Quad I = is the angle itself cos( u cosucosv uv Quad II = 80 θ o π - θ cos( u cosucosv uv Quad III = θ 80 o θ - π Quad IV = 60 θ o π - θ u ( u u u ( u u Saved C: Tigonomet Fomulas {Web Page} micosoftwod & PDF Website: www.mathgaphs.com
Recipocal Identities csc csc Ratio o Quotient Identities cos cot cos cos sec sec cos = cos cos = cot cot cot Pthagoean Identities Pthagoean Identities in Radical Fom cos cos sec cot csc sec Note: thee ae onl thee, basic Pthagoean identities, the othe foms ae the same thee identities, just aanged in a diffeent ode. sec Confunction Identities Odd-Even Identities lso called negative angle identities cos cos Sin (-) = - Csc (-) = -csc Cos (-) = cos Sec (-) = sec cot cot Tan (-) = - Cot (-) = -cot csc csc sec Sum and Diffeence Fomulas - Identities ( u ucosv cosuv cos( u cosucosv uv ( u ucosv cosuv cos( u cosucosv uv ( u u u u ( u u Saved C: Tigonomet Fomulas {Web Page} micosoftwod & PDF Website: www.mathgaphs.com
The Unit Cicle 90 Tan = - cot = undefined & cot= 0 = cot = 0 60 Tan = Tan =- - cot = Cot = - 5 45.09.57.04 50.5 0.785.6 Tan = cot = -.5 = cot = Tan= 0 Cot=undef Tan.4 80 60.66 (.4 )= 6.8 Tan=0 & cot=undef cot =.95 5.75 = cot = - 4.86 5.49 4.7 5. 0 0 Tan = - Tan = Cot = - Cot = 5 5 Tan = cot = 40 70 00 =undefined = - cot = Cot = 0 Definition of Tigonometic Functions concening the Unit Cicle θ = hp csc θ = hp cos θ = hp sec θ = hp θ = cot θ = Saved C: Tigonomet Fomulas {Web Page} micosoftwod & PDF Website: www.mathgaphs.com
Right Tiangle Definitions of Tigonometic Functions Note: & cos ae complementa angles, so ae & cot and sec & cos, and the sum of complementa angles is 90 degees. θ = hp cos θ = hp θ = csc θ = hp sec θ = hp cot θ = Hpotenuse C B acent djacent = is the side acent to the angle in consideation. So if we ae consideing ngle, then the acent side is CB osite Tigonometic Values of Special ngles Degees 0 0 45 60 90 80 70 Radians 0 6 4 θ 0 0 - cosθ 0-0 θ 0 undefined 0 undefined To Convet Degees to Radians, Multipl b To Convet Radians to Degees, Multipl b ad 80deg 80deg ad Vocabula Cogent ngles - ae two angles with the same teminal side Refeence ngle - is an acute angle fomed b teminal side of angle(α) with -ais Saved C: Tigonomet Fomulas {Web Page} micosoftwod & PDF Website: www.mathgaphs.com 4
Double ngle Identities Half ngle Identities Powe Reducing Fomulas cos cosu cos u cos cos cos cos cosu cos u cos cos cos cos cos u u cosu cos Poduct-to-Sum Fomulas u v cos( u cos( u cosucosv cos( u cos( u ucosv ( u ( u cosuv ( u ( u Law of Sines Solving Oblique Tiangles ug e: S, S, SS, SSS, SS Sum-to-Poduct Fomulas cos cos cos cos cos cos cos cos Law of Coes Coe: SS, SSS a b c o B C Sdad Fom ltenative Fom B C a b c bccos cos b c a a b c bc b a c accos B cos B a c b ac c b a abcos C cosc a b c ab ea of an Oblique Tiangle Finding the ea of non-90degee Tiangles aea bc ab C ac B Step : Find s Heon s Fomula a b c Saved C: Tigonomet Fomulas {Web Page} micosoftwod & PDF Website: www.mathgaphs.com 5 s Step : Use the fomula aea s( s a)( s b)( s c)