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Pertanyaan

Nilai dari  adalah ....

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F. Ayudhita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat!

begin mathsize 14px style tan invisible function application a equals fraction numerator sin invisible function application a over denominator cos invisible function application a end fraction end style 

Perhatikan perhitungan berikut!

begin mathsize 14px style sin invisible function application 45 degree equals 1 half square root of 2 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 330 degree end cell equals cell cos invisible function application left parenthesis 360 degree minus 30 degree right parenthesis space end cell row blank equals cell cos invisible function application 30 degree end cell row blank equals cell 1 half square root of 3 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application 240 degree end cell equals cell tan invisible function application open parentheses 180 degree plus 60 degree close parentheses end cell row blank equals cell tan invisible function application 60 degree end cell row blank equals cell fraction numerator sin invisible function application 60 degree over denominator cos invisible function application 60 degree end fraction end cell row blank equals cell fraction numerator 1 half square root of 3 blank over denominator 1 half end fraction end cell row blank equals cell square root of 3 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin invisible function application 150 degree end cell equals cell sin invisible function application open parentheses 180 degree minus 30 degree close parentheses end cell row blank equals cell sin invisible function application 30 degree end cell row blank equals cell 1 half end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos invisible function application 225 degree end cell equals cell negative cos invisible function application open parentheses 180 degree plus 45 degree close parentheses end cell row blank equals cell negative cos invisible function application 45 degree end cell row blank equals cell negative 1 half square root of 2 end cell end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan invisible function application 315 degree end cell equals cell negative tan invisible function application open parentheses 360 degree minus 45 degree close parentheses end cell row blank equals cell negative tan invisible function application 45 degree end cell row blank equals cell negative 1 end cell end table end style 

Dengan demikian, diperoleh perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin invisible function application 45 degree cos invisible function application 330 degree tan invisible function application 240 degree over denominator sin invisible function application 150 degree cos invisible function application 225 degree tan invisible function application 315 degree end fraction end cell row blank equals cell fraction numerator left parenthesis 1 half square root of 2 right parenthesis left parenthesis 1 half square root of 3 right parenthesis left parenthesis square root of 3 right parenthesis over denominator left parenthesis 1 half right parenthesis left parenthesis negative 1 half square root of 2 right parenthesis left parenthesis negative 1 right parenthesis end fraction end cell row blank equals 3 end table end style   

Jadi, jawaban yang tepat adalah E.

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