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Diketahui Nilai dari a + b adalah ....

Diketahui open parentheses table row a row b end table close parentheses equals 1 over 2 to the power of 50 open parentheses table row cell square root of 2 end cell cell negative square root of 2 end cell row cell square root of 2 end cell cell square root of 2 end cell end table close parentheses to the power of 20 open parentheses table row 1 cell negative square root of 3 end cell row cell square root of 3 end cell 1 end table close parentheses to the power of 30 open parentheses table row 1 row cell negative 1 end cell end table close parentheses. Nilai dari  adalah ....

  1. negative 2

  2. negative 1

  3.  

  4. 1

  5. 2

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N. Syafriah

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

jawaban yang tepat adalah C.

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Pembahasan

Perhatikan perhitungan berikut ini! Dapat dilihat bahwa perkalian matriks di atas tersusun dari perkalian-perkalian dengan matriks rotasi. Kemudian, perhatikan dua sifat matriks rotasi berikut! Oleh karena itu, didapat hasil perhitungan sebagai berikut. Selanjutnya, perhatikan bahwa dan dengan adalah bilangan bulat. Oleh karena itu, didapat hasil perhitungan sebagai berikut. Dengan demikian, nilai dari . Jadi, jawaban yang tepat adalah C.

Perhatikan perhitungan berikut ini!

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row a row b end table close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 2 to the power of 50 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell square root of 2 end cell cell negative square root of 2 end cell row cell square root of 2 end cell cell square root of 2 end cell end table close parentheses end cell end table to the power of 20 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 1 cell negative square root of 3 end cell row cell square root of 3 end cell 1 end table close parentheses end cell end table to the power of 30 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 1 row cell negative 1 end cell end table close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row a row b end table close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 2 to the power of 20 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell square root of 2 end cell cell negative square root of 2 end cell row cell square root of 2 end cell cell square root of 2 end cell end table close parentheses end cell end table to the power of 20 table attributes columnalign right center left columnspacing 0px end attributes row blank blank times end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 2 to the power of 30 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 1 cell negative square root of 3 end cell row cell square root of 3 end cell 1 end table close parentheses end cell end table to the power of 30 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 1 row cell negative 1 end cell end table close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row a row b end table close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell 1 half square root of 2 end cell cell negative 1 half square root of 2 end cell row cell 1 half square root of 2 end cell cell 1 half square root of 2 end cell end table close parentheses end cell end table to the power of 20 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell 1 half end cell cell negative 1 half square root of 3 end cell row cell 1 half square root of 3 end cell cell 1 half end cell end table close parentheses end cell end table to the power of 30 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 1 row cell negative 1 end cell end table close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row a row b end table close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell cos invisible function application 45 degree end cell cell negative sin invisible function application 45 degree end cell row cell sin invisible function application 45 degree end cell cell cos invisible function application 45 degree end cell end table close parentheses end cell end table to the power of 20 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell cos invisible function application 60 degree end cell cell negative sin invisible function application 60 degree end cell row cell sin invisible function application 60 degree end cell cell cos invisible function application 60 degree end cell end table close parentheses end cell end table to the power of 30 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row 1 row cell negative 1 end cell end table close parentheses end cell end table end style

Dapat dilihat bahwa perkalian matriks di atas tersusun dari perkalian-perkalian dengan matriks rotasi.

Kemudian, perhatikan dua sifat matriks rotasi berikut!

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses table row cell cos invisible function application alpha end cell cell negative sin invisible function application alpha end cell row cell sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close parentheses open parentheses table row cell cos invisible function application beta end cell cell negative sin invisible function application beta end cell row cell sin invisible function application beta end cell cell cos invisible function application beta end cell end table close parentheses end cell equals cell open parentheses table row cell cos invisible function application open parentheses alpha plus beta close parentheses end cell cell negative sin invisible function application open parentheses alpha plus beta close parentheses end cell row cell sin invisible function application open parentheses alpha plus beta close parentheses end cell cell cos invisible function application open parentheses alpha plus beta close parentheses end cell end table close parentheses end cell row cell open parentheses table row cell cos invisible function application alpha end cell cell negative sin invisible function application alpha end cell row cell sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close parentheses to the power of n end cell equals cell open parentheses table row cell cos invisible function application n alpha end cell cell negative sin invisible function application n alpha end cell row cell sin invisible function application n alpha end cell cell cos invisible function application n alpha end cell end table close parentheses end cell end table

Oleh karena itu, didapat hasil perhitungan sebagai berikut.

begin mathsize 12px style open parentheses table row a row b end table close parentheses equals open parentheses table row cell cos invisible function application 45 degree end cell cell negative sin invisible function application 45 degree end cell row cell sin invisible function application 45 degree end cell cell cos invisible function application 45 degree end cell end table close parentheses to the power of 20 open parentheses table row cell cos invisible function application 60 degree end cell cell negative sin invisible function application 60 degree end cell row cell sin invisible function application 60 degree end cell cell cos invisible function application 60 degree end cell end table close parentheses to the power of 30 open parentheses table row 1 row cell negative 1 end cell end table close parentheses open parentheses table row a row b end table close parentheses equals open parentheses table row cell cos invisible function application left parenthesis 20 times 45 degree right parenthesis end cell cell negative sin invisible function application left parenthesis 20 times 45 degree right parenthesis end cell row cell sin invisible function application left parenthesis 20 times 45 degree right parenthesis end cell cell cos invisible function application left parenthesis 20 times 45 degree right parenthesis end cell end table close parentheses open parentheses table row cell cos invisible function application left parenthesis 30 times 60 degree right parenthesis end cell cell negative sin invisible function application left parenthesis 30 times 60 degree right parenthesis end cell row cell sin invisible function application left parenthesis 30 times 60 degree right parenthesis end cell cell cos invisible function application left parenthesis 30 times 60 degree right parenthesis end cell end table close parentheses open parentheses table row 1 row cell negative 1 end cell end table close parentheses open parentheses table row a row b end table close parentheses equals open parentheses table row cell cos invisible function application 900 degree end cell cell negative sin invisible function application 900 degree end cell row cell sin invisible function application 900 degree end cell cell cos invisible function application 900 degree end cell end table close parentheses open parentheses table row cell cos invisible function application 1.800 to the power of o end cell cell negative sin invisible function application 1.800 end cell row cell sin invisible function application 1.800 to the power of o end cell cell cos invisible function application 1.800 end cell end table close parentheses open parentheses table row 1 row cell negative 1 end cell end table close parentheses open parentheses table row a row b end table close parentheses equals open parentheses table row cell cos invisible function application open parentheses 900 degree plus 1.800 degree close parentheses end cell cell negative sin invisible function application open parentheses 900 degree plus 1.800 degree close parentheses end cell row cell sin invisible function application open parentheses 900 degree plus 1.800 degree close parentheses end cell cell cos invisible function application open parentheses 900 degree plus 1.800 degree close parentheses end cell end table close parentheses open parentheses table row 1 row cell negative 1 end cell end table close parentheses open parentheses table row a row b end table close parentheses equals open parentheses table row cell cos invisible function application 2.700 degree end cell cell negative sin invisible function application 2.700 degree end cell row cell sin invisible function application 2.700 degree end cell cell cos invisible function application 2.700 degree end cell end table close parentheses open parentheses table row 1 row cell negative 1 end cell end table close parentheses end style

Selanjutnya, perhatikan bahwa begin mathsize 14px style sin invisible function application open parentheses 360 to the power of o k plus x to the power of o close parentheses equals sin invisible function application x to the power of o end style dan begin mathsize 14px style cos invisible function application open parentheses 360 to the power of o k plus x to the power of o close parentheses equals cos invisible function application x to the power of o end style dengan k adalah bilangan bulat. Oleh karena itu, didapat hasil perhitungan sebagai berikut.

begin mathsize 12px style open parentheses table row a row b end table close parentheses equals open parentheses table row cell cos invisible function application 2.700 degree end cell cell negative sin invisible function application 2.700 degree end cell row cell sin invisible function application 2.700 degree end cell cell cos invisible function application 2.700 degree end cell end table close parentheses open parentheses table row 1 row cell negative 1 end cell end table close parentheses open parentheses table row a row b end table close parentheses equals open parentheses table row cell cos invisible function application left parenthesis 360 degree times 7 plus 180 degree right parenthesis end cell cell negative sin invisible function application left parenthesis 360 degree times 7 plus 180 degree right parenthesis end cell row cell sin invisible function application left parenthesis 360 degree times 7 plus 180 degree right parenthesis end cell cell cos invisible function application left parenthesis 360 degree times 7 plus 180 degree right parenthesis end cell end table close parentheses open parentheses table row 1 row cell negative 1 end cell end table close parentheses open parentheses table row a row b end table close parentheses equals open parentheses table row cell cos invisible function application 180 degree end cell cell negative sin invisible function application 180 degree end cell row cell sin invisible function application 180 degree end cell cell cos invisible function application 180 degree end cell end table close parentheses open parentheses table row 1 row cell negative 1 end cell end table close parentheses open parentheses table row a row b end table close parentheses equals open parentheses table row cell negative 1 end cell 0 row 0 cell negative 1 end cell end table close parentheses open parentheses table row 1 row cell negative 1 end cell end table close parentheses open parentheses table row a row b end table close parentheses equals open parentheses table row cell negative 1 end cell row 1 end table close parentheses end style

Dengan demikian, nilai dari a plus b equals left parenthesis negative 1 right parenthesis plus 1 equals 0.

Jadi, jawaban yang tepat adalah C.

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