Transcription of Trigonometric Formula Sheet De nition of the Trig Functions
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Trigonometric Formula Sheet De nition of the Trig Functions
Trigonometric Formula SheetDefinition of the Trig FunctionsRight Triangle DefinitionAssume that:0< < 2or 0 < <90 hypotenuseadjacentopposite sin =opphypcsc =hypoppcos =adjhypsec =hypadjtan =oppadjcot =adjoppUnit Circle DefinitionAssume can be any (x,y) sin =y1csc =1ycos =x1sec =1xtan =yxcot =xyDomains of the Trig Functionssin , ( , )cos , ( , )tan , 6=(n+12) , where n Zcsc , 6=n , where n Zsec , 6=(n+12) , where n Zcot , 6=n , where n ZRanges of the Trig Functions 1 sin 1 1 cos 1 tan csc 1andcsc 1sec 1andsec 1 cot Periods of the Trig FunctionsThe period of a function is the number, T, such that f ( +T ) = f ( ) .So, if is a fixed number and is any angle we have the following ( ) T=2 cos( ) T=2 tan( ) T= csc( ) T=2 sec( ) T=2 cot( ) T= 1 Identities and FormulasTangent and Cotangent Identitiestan =sin cos cot =cos sin Reciprocal Identitiessin =1csc csc =1sin cos =1sec sec =1cos tan =1cot cot =1tan Pythagorean Identitiessin2 + cos2 = 1tan2 + 1 = sec2 1 + cot2 = csc2 Even and Odd Formulassin( ) = sin cos( ) = cos tan( ) = tan csc( ) = csc sec( ) = sec cot( ) = cot Periodic FormulasIf n is an integersin( + 2 n) = sin cos( + 2 n) = cos tan( + n) = tan csc( + 2 n) = csc sec( + 2 n) = sec cot( + n) = cot Double Angle Formulassin(2 ) = 2 sin cos cos(2 ) = cos2
Double Angle Formulas sin(2 ) = 2sin cos cos(2 ) = cos2 sin2 = 2cos2 1 = 1 2sin2 tan(2 ) = 2tan 1 tan2 Degrees to Radians Formulas If x is an angle in degrees and t is an angle in radians then: ˇ 180 = t x) t= ˇx 180 and x= 180 t ˇ Half Angle Formulas sin = r 1 cos(2 ) 2 cos = r 1 + cos(2 ) 2 tan = s 1 cos(2 ) 1 + cos(2 ) Sum and Di erence ...
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