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Pertanyaan

sin space 37 comma 5 degree space sin space 7 comma 5 degree equals...

  1. square root of 2 minus square root of 3

  2. 1 half square root of 2 minus 1 half square root of 3

  3. 1 fourth square root of 2 minus 1 fourth square root of 3

  4. 1 fourth square root of 3 minus 1 fourth square root of 2

  5. 1 half square root of 3 minus 1 half square root of 2

Pembahasan Soal:

Untuk menyelesaikan soal tersebut kita dapat menggunakan rumus perkalian trigonometri:

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 space sin space A space sin space B end cell equals cell cos space left parenthesis A plus B right parenthesis minus cos space left parenthesis A minus B right parenthesis end cell row cell sin space A space sin space B end cell equals cell fraction numerator cos space left parenthesis A minus B right parenthesis minus cos space left parenthesis A plus B right parenthesis over denominator 2 end fraction end cell end table

Tabel sudut istimewa:

Pembahasan:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 37 comma 5 degree space sin space 7 comma 5 degree end cell equals cell fraction numerator cos space left parenthesis 37 comma 5 degree minus 7 comma 5 degree right parenthesis minus cos space left parenthesis 37 comma 5 degree plus 7 comma 5 degree right parenthesis over denominator 2 end fraction end cell row blank equals cell fraction numerator cos space 30 degree minus cos space 45 degree over denominator 2 end fraction end cell row blank equals cell fraction numerator begin display style 1 half end style square root of 3 minus begin display style 1 half end style square root of 2 over denominator 2 end fraction end cell row blank equals cell 1 fourth square root of 3 minus 1 fourth square root of 2 end cell end table end style

Oleh karena itu, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

O. Rahmawati

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Terakhir diupdate 11 Juli 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Nyatakan sebagai jumlah atau selisih kosinus, dan sederhanakanlah jika mungkin. d.

Pembahasan Soal:

Ingat kembali:

2 space sin space straight alpha space sin space straight beta equals negative cos space open parentheses straight alpha plus straight beta close parentheses plus cos space open parentheses straight alpha minus straight beta close parentheses 

Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space sin space open parentheses straight A plus straight B minus straight C close parentheses space sin space open parentheses straight A minus straight B plus straight C close parentheses end cell equals cell negative cos space open parentheses open parentheses straight A plus straight B minus straight C close parentheses plus open parentheses straight A minus straight B plus straight C close parentheses close parentheses plus cos space open parentheses open parentheses straight A plus straight B minus straight C close parentheses minus open parentheses straight A minus straight B plus straight C close parentheses close parentheses end cell row blank equals cell negative cos space open parentheses straight A up diagonal strike plus straight B end strike up diagonal strike negative straight C end strike plus straight A up diagonal strike negative straight B end strike up diagonal strike plus straight C end strike close parentheses plus cos space open parentheses up diagonal strike straight A plus straight B minus straight C up diagonal strike negative straight A end strike plus straight B minus straight C close parentheses end cell row blank equals cell negative cos space 2 straight A plus cos space open parentheses 2 straight B minus 2 straight C close parentheses end cell end table end style 

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses straight A plus straight B minus straight C close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses straight A minus straight B plus straight C 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight A end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 2 straight B minus 2 straight C close parentheses end cell end table.

0

Roboguru

Ekspresi trigonometri sin10∘⋅sin50∘⋅sin70∘ akan setara dengan ekspresi trigonometri . . . .

Pembahasan Soal:

Ingat konsep trigonometri sinA=cos(90A)untuk0A90.

Dengan menggunakan konsep tersebut, diperoleh:

sin10sin50sin70===cos(9010)cos(9050)cos(9070)cos80cos40cos20cos20cos40cos80

Jadi, sin10sin50sin70=cos20cos40cos80.

Oleh karena itu, jawaban yang benar adalah E.

0

Roboguru

Hitunglah:

Pembahasan Soal:

Ingat bahwa: 

  • 2 space sin space a space sin space b equals negative cos space left parenthesis a plus b right parenthesis plus cos space left parenthesis a minus b right parenthesis 

Mencari nilai dari sin space 52 degree space sin space 68 degree minus sin space 13 degree space sin space 47 degree minus sin space 9 degree space sin space 25 degree, Didapat:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses minus sin open parentheses 13 degree close parentheses sin open parentheses 47 degree close parentheses minus sin open parentheses 9 degree close parentheses sin open parentheses 25 degree close parentheses end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses minus sin open parentheses 13 degree close parentheses sin open parentheses 47 degree close parentheses end cell row blank blank cell negative fraction numerator negative cos open parentheses 9 degree plus 25 degree close parentheses plus cos open parentheses 9 degree minus 25 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses minus sin open parentheses 13 degree close parentheses sin open parentheses 47 degree close parentheses end cell row blank blank cell negative fraction numerator negative cos open parentheses 34 degree close parentheses plus cos open parentheses negative 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses minus sin open parentheses 13 degree close parentheses sin open parentheses 47 degree close parentheses end cell row blank blank cell negative fraction numerator negative cos open parentheses 34 degree close parentheses plus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses end cell row blank blank cell negative fraction numerator negative cos open parentheses 13 degree plus 47 degree close parentheses plus cos open parentheses 13 degree minus 47 degree close parentheses over denominator 2 end fraction end cell row blank blank cell negative fraction numerator negative cos open parentheses 34 degree close parentheses plus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses end cell row blank blank cell plus fraction numerator cos open parentheses 60 degree close parentheses minus cos open parentheses 34 degree close parentheses plus cos open parentheses 34 degree close parentheses minus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses plus fraction numerator cos open parentheses 60 degree close parentheses minus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses plus fraction numerator 1 half minus cos open parentheses 16 degree close parentheses over denominator 2 end fraction end cell row blank equals cell sin open parentheses 52 degree close parentheses sin open parentheses 68 degree close parentheses plus fraction numerator 1 minus 2 cos open parentheses 16 degree close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative cos open parentheses 52 degree plus 68 degree close parentheses plus cos open parentheses 52 degree minus 68 degree close parentheses over denominator 2 end fraction end cell row blank blank cell plus fraction numerator 1 minus 2 cos open parentheses 16 degree close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative cos open parentheses 120 degree close parentheses plus cos open parentheses negative 16 degree close parentheses over denominator 2 end fraction plus fraction numerator 1 minus 2 cos open parentheses 16 degree close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative cos open parentheses 120 degree close parentheses plus cos open parentheses 16 degree close parentheses over denominator 2 end fraction plus fraction numerator 1 minus 2 cos open parentheses 16 degree close parentheses over denominator 4 end fraction end cell row blank equals cell fraction numerator negative 2 open parentheses negative 1 half close parentheses plus 1 over denominator 4 end fraction end cell row blank equals cell 1 half end cell end table  

Jadi, nilai dari sin space 52 degree space sin space 68 degree minus sin space 13 degree space sin space 47 degree minus sin space 9 degree space sin space 25 degree adalah 1 half.

0

Roboguru

Ekspresi trigonometri 4sin50∘⋅sin65∘⋅sin65∘ sama dengan . . . .

Pembahasan Soal:

Ingat rumus perkalian trigonometri berikut ini:

2sinAsinB=cos(A+B)cos(AB)

2cosAsinB=sin(A+B)sin(AB)

Dengan menggunakan konsep di atas, diperoleh hasil:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 blank sin space 50 degree space sin space 65 degree space sin space 65 degree end cell equals cell 2 blank sin space 50 degree open parentheses 2 space sin space 65 degree space sin space 65 degree close parentheses end cell row blank equals cell 2 blank sin space 50 degree open parentheses negative cos space open parentheses 65 degree plus 65 degree close parentheses plus cos space open parentheses 65 degree minus 65 degree close parentheses close parentheses end cell row blank equals cell 2 blank sin space 50 degree open parentheses negative cos space 130 degree plus cos space 0 degree close parentheses end cell row blank equals cell 2 blank sin space 50 degree open parentheses negative cos space 130 degree plus 1 close parentheses end cell row blank equals cell negative 2 cos space 130 degree blank sin space 50 degree plus 2 blank sin space 50 degree end cell row blank equals cell negative sin space open parentheses 130 degree plus 50 degree close parentheses plus sin space open parentheses 130 degree minus 50 degree close parentheses plus 2 blank sin space 50 degree end cell row blank equals cell negative sin space 180 degree plus sin space 80 degree plus 2 blank sin space 50 degree end cell row blank equals cell 0 plus sin space 80 degree plus 2 blank sin space 50 degree end cell row blank equals cell sin space 80 degree plus 2 blank sin space 50 degree end cell end table

Jadi, 4 space sin space 50 degree times sin space 65 degree times sin space 65 degree 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 sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 80 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 50 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table.

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Tanpa menggunakan kalkulator atau tabel trigonometri, hitunglah:

Pembahasan Soal:

Ingat kembali:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space sin space straight alpha space sin space straight beta end cell equals cell negative cos space open parentheses straight alpha plus straight beta close parentheses plus cos space open parentheses straight alpha minus straight beta close parentheses end cell row cell 2 space sin space straight alpha space cos space straight beta end cell equals cell sin space open parentheses straight alpha plus straight beta close parentheses plus sin space open parentheses straight alpha minus straight beta close parentheses end cell row cell sin space open parentheses 180 degree minus straight A close parentheses end cell equals cell sin space straight A end cell end table 

Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 8 space sin space 70 degree times sin space 50 degree times sin space 10 degree end cell equals cell 4 times 2 times sin space 70 degree times sin space 50 degree times sin space 10 degree end cell row blank equals cell open parentheses 4 times sin space 70 degree close parentheses times open parentheses 2 times sin space 50 degree times sin space 10 degree close parentheses end cell row blank equals cell open parentheses 4 times sin space 70 degree close parentheses times open parentheses negative cos space open parentheses 50 degree plus 10 degree close parentheses plus cos space open parentheses 50 degree minus 10 degree close parentheses close parentheses end cell row blank equals cell open parentheses 4 times sin space 70 degree close parentheses times open parentheses negative cos space 60 degree plus cos space 40 degree close parentheses end cell row blank equals cell open parentheses 4 times sin space 70 degree close parentheses times open parentheses negative 1 half plus cos space 40 degree close parentheses end cell row blank equals cell negative 2 space sin space 70 degree plus 4 times sin space 70 degree times cos space 40 degree end cell row blank equals cell negative 2 space sin space 70 degree plus 2 times open parentheses 2 times sin space 70 degree times cos space 40 degree close parentheses end cell row blank equals cell negative 2 space sin space 70 degree plus 2 times open parentheses sin space open parentheses 70 degree plus 40 degree close parentheses plus sin space open parentheses 70 degree minus 40 degree close parentheses close parentheses end cell row blank equals cell negative 2 space sin space 70 degree plus 2 times open parentheses sin space 110 degree plus sin space 30 degree close parentheses end cell row blank equals cell negative 2 space sin space 70 degree plus 2 times open parentheses sin space 110 degree plus 1 half close parentheses end cell row blank equals cell negative 2 space sin space 70 degree plus 2 space sin space 110 degree plus 1 end cell row blank equals cell negative 2 space sin space 70 degree plus 2 space sin space open parentheses 180 degree minus 70 degree close parentheses plus 1 end cell row blank equals cell up diagonal strike negative 2 space sin space 70 degree end strike up diagonal strike plus 2 space sin space 70 degree end strike plus 1 end cell row blank equals 1 end table end style 

Jadi, nilai table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 70 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table 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 sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 50 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table 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 sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 10 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree 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 1 end table.

0

Roboguru

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