Roboguru

Pertanyaan

2 sin space A space cos space B equals....

  1. cos open parentheses A and B close parentheses plus cos open parentheses A bond B close parentheses

  2. cos open parentheses A and B close parentheses minus sign cos open parentheses A bond B close parentheses

  3. sin open parentheses A and B close parentheses plus sin open parentheses A bond B close parentheses

  4. sin open parentheses A and B close parentheses minus sign sin open parentheses A bond B close parentheses

  5. sin open parentheses A and B close parentheses plus cos open parentheses A bond B close parentheses

Pembahasan Soal:

Rumus perkalian fungsi trigonometri sinus dan cosinus

2 sin space A space cos space B double bond sin open parentheses A and B close parentheses minus sign sin open parentheses A bond B close parentheses

Jadi, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Umi

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Pembahasan Soal:

Rumus perkalian sinus dan kosinus adalah sebagai berikut.

open parentheses straight i close parentheses space space 2 space sin space A space cos space B equals sin space open parentheses A plus B close parentheses plus sin space open parentheses A minus B close parentheses left parenthesis ii right parenthesis space space 2 space cos space A space sin space B equals sin space open parentheses A plus B close parentheses minus sin space open parentheses A minus B close parentheses left parenthesis iii right parenthesis space 2 space cos space A space cos space B equals cos space open parentheses A plus B close parentheses plus cos space open parentheses A minus B close parentheses left parenthesis iv right parenthesis space 2 space sin space A space sin space B equals cos space open parentheses A minus B close parentheses minus cos space open parentheses A plus B close parentheses

Berdasarkan rumus no (i) dan (ii) di atas, maka:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses sin space 75 degree space cos space 15 degree close parentheses minus open parentheses cos space 75 degree space sin space 15 degree close parentheses end cell row blank equals cell 1 half open parentheses sin space open parentheses 75 degree plus 15 degree close parentheses plus sin space open parentheses 75 degree minus 15 degree close parentheses close parentheses end cell row blank blank cell negative 1 half space open parentheses sin space open parentheses 75 degree plus 15 degree close parentheses minus sin space open parentheses 75 degree minus 15 degree close parentheses close parentheses end cell row blank equals cell 1 half open parentheses space sin space 90 degree plus sin space 60 degree close parentheses minus 1 half open parentheses sin space 90 degree minus sin space 60 degree close parentheses end cell row blank equals cell 1 half open parentheses 1 plus 1 half square root of 3 close parentheses minus 1 half open parentheses 1 minus 1 half square root of 3 close parentheses end cell row blank equals cell 1 half plus 1 fourth square root of 3 minus 1 half plus 1 fourth square root of 3 end cell row blank equals cell 2 over 4 square root of 3 end cell row blank equals cell 1 half square root of 3 end cell end table

Dengan demikian, hasil dari open parentheses sin space 75 degree space cos space 15 degree close parentheses minus open parentheses cos space 75 degree space sin space 15 degree close parentheses adalah 1 half square root of 3.

Oleh karena itu, jawaban yang benar adalah D.

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.

Roboguru

Pembahasan Soal:

Untuk menyelesaikan soal tersebut kita bisa menggunakan rumus perkalian trigonometri:

2 space sin space A space cos space B equals sin space open parentheses A plus B close parentheses plus space sin space open parentheses A minus B close parentheses

Tabel sudut istimewa:

Pembahasan:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space sin space 52 comma 5 degree space cos space 7 comma 5 degree end cell equals cell sin space open parentheses 52 comma 5 degree plus 7 comma 5 degree close parentheses plus space sin space open parentheses 52 comma 5 degree minus 7 comma 5 degree close parentheses end cell row blank equals cell sin space 60 degree plus sin space 45 degree end cell row blank equals cell 1 half square root of 3 plus 1 half square root of 2 end cell row blank equals cell 1 half open parentheses square root of 3 plus square root of 2 close parentheses end cell end table end style

Oleh karena itu, jawaban yang benar adalah C.

Roboguru

Tanpa menggunakan tabel trigonometri, buktikan:

Pembahasan Soal:

Ingat kembali:

2 space sin space straight alpha space cos space straight beta equals sin space open parentheses straight alpha plus straight beta close parentheses plus sin space open parentheses straight alpha minus straight beta close parentheses 2 space cos space straight alpha space cos space straight beta equals cos space open parentheses straight alpha plus straight beta close parentheses minus cos space open parentheses straight alpha minus straight beta close parentheses 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 sin space open parentheses 180 degree minus straight A close parentheses equals sin space straight A cos space open parentheses 90 degree plus straight A close parentheses equals negative sin space straight A 

Akan dibuktikan sin space 52 degree space sin space 68 degree minus sin space 47 degree space cos space 77 degree minus cos space 65 degree space cos space 81 degree equals 1 half. Maka:

 begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell sin space 52 degree space sin space 68 degree minus sin space 47 degree space cos space 77 degree minus cos space 65 degree space cos space 81 degree end cell row blank equals cell 1 half times 2 times sin space 52 degree space sin space 68 degree minus 1 half times 2 times sin space 47 degree space cos space 77 degree minus 1 half times 2 times cos space 65 degree space cos space 81 degree end cell row blank equals cell 1 half times open parentheses 2 times sin space 52 degree space sin space 68 degree close parentheses minus 1 half times open parentheses 2 times sin space 47 degree space cos space 77 degree close parentheses minus 1 half times open parentheses 2 times cos space 65 degree space cos space 81 degree close parentheses end cell row blank equals cell 1 half open square brackets negative cos space open parentheses 52 degree plus 68 degree close parentheses plus cos space open parentheses 52 degree minus 68 degree close parentheses close square brackets minus 1 half open square brackets sin space open parentheses 47 degree plus 77 degree close parentheses plus sin space open parentheses 47 degree minus 77 degree close parentheses close square brackets minus 1 half open square brackets cos space open parentheses 65 degree plus 81 degree close parentheses plus cos space open parentheses 65 degree minus 81 degree close parentheses close square brackets end cell row blank equals cell 1 half open square brackets negative cos space 120 degree plus cos space open parentheses negative 16 degree close parentheses close square brackets minus 1 half open square brackets sin space 124 degree plus sin space open parentheses negative 30 degree close parentheses close square brackets minus 1 half open square brackets cos space 146 degree plus cos space open parentheses negative 16 degree close parentheses close square brackets end cell row blank equals cell 1 half open square brackets negative open parentheses negative 1 half close parentheses minus cos space 16 degree close square brackets minus 1 half open square brackets sin space 124 degree minus sin space 30 degree close square brackets minus 1 half open square brackets cos space 146 degree minus cos space 16 degree close square brackets end cell row blank equals cell 1 half open square brackets 1 half minus cos space 16 degree close square brackets minus 1 half open square brackets sin space 124 degree minus 1 half close square brackets minus 1 half open square brackets cos space 146 degree minus cos space 16 degree close square brackets end cell row blank equals cell 1 half open parentheses 1 half up diagonal strike negative cos space 16 degree end strike minus sin space 124 degree plus 1 half minus cos space 146 degree up diagonal strike plus cos space 16 end strike degree close parentheses end cell row blank equals cell 1 half open parentheses 1 minus sin space 124 degree minus cos space 146 degree close parentheses end cell row blank equals cell 1 half open parentheses 1 minus open parentheses sin space 124 degree plus cos space 146 degree close parentheses close parentheses end cell row blank equals cell 1 half open parentheses 1 minus open parentheses sin space open parentheses 180 degree minus 56 degree close parentheses plus cos space open parentheses 90 degree plus 56 degree close parentheses close parentheses close parentheses end cell row blank equals cell 1 half open parentheses 1 minus open parentheses up diagonal strike sin space 56 degree end strike up diagonal strike negative sin space 56 degree end strike close parentheses close parentheses end cell row blank equals cell 1 half open parentheses 1 minus 0 close parentheses end cell row blank equals cell 1 half open parentheses 1 close parentheses end cell row blank equals cell 1 half end cell end table end style

Jadi, terbukti bahwa sin space 52 degree space sin space 68 degree minus sin space 47 degree space cos space 77 degree minus cos space 65 degree space cos space 81 degree equals 1 half.

Roboguru

Buktikan:

Pembahasan Soal:

Ingat kembali:

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

Akan dibuktikan begin mathsize 12px style 2 space sin space 1 half straight theta space cos space 3 over 2 straight theta plus 2 space sin space 5 over 2 straight theta space cos space 3 over 2 straight theta plus 2 space sin space 3 over 2 straight theta space cos space 7 over 2 straight theta equals sin space 4 straight theta plus sin space 5 straight theta end style. Maka: begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell Ruas space kiri end cell equals cell 2 space sin space 1 half straight theta space cos space 3 over 2 straight theta plus 2 space sin space 5 over 2 straight theta space cos space 3 over 2 straight theta plus 2 space sin space 3 over 2 straight theta space cos space 7 over 2 straight theta end cell row blank equals cell open square brackets sin space open parentheses 1 half straight theta plus 3 over 2 straight theta close parentheses plus sin space open parentheses 1 half straight theta minus 3 over 2 straight theta close parentheses close square brackets plus open square brackets sin space open parentheses 5 over 2 straight theta plus 3 over 2 straight theta close parentheses plus sin space open parentheses 5 over 2 straight theta minus 3 over 2 straight theta close parentheses close square brackets plus open square brackets sin space open parentheses 3 over 2 straight theta plus 7 over 2 straight theta close parentheses plus sin space open parentheses 3 over 2 straight theta minus 7 over 2 straight theta close parentheses close square brackets end cell row blank equals cell open square brackets sin space open parentheses 4 over 2 straight theta close parentheses plus sin space open parentheses negative 2 over 2 straight theta close parentheses close square brackets plus open square brackets sin space open parentheses 8 over 2 straight theta close parentheses plus sin space open parentheses 2 over 2 straight theta close parentheses close square brackets plus open square brackets sin space open parentheses 10 over 2 straight theta close parentheses plus sin space open parentheses negative 4 over 2 straight theta close parentheses close square brackets end cell row blank equals cell open parentheses sin space 2 straight theta minus sin space straight theta close parentheses plus open parentheses sin space 4 straight theta plus sin space straight theta close parentheses plus open parentheses sin space 5 straight theta minus sin space 2 straight theta close parentheses end cell row blank equals cell up diagonal strike sin space 2 straight theta end strike up diagonal strike negative sin space straight theta end strike plus sin space 4 straight theta up diagonal strike plus sin space straight theta end strike plus sin space 5 straight theta up diagonal strike negative sin space 2 straight theta end strike end cell row blank equals cell sin space 4 straight theta plus sin space 5 straight theta end cell end table end style  

Jadi, terbukti bahwa begin mathsize 12px style 2 space sin space 1 half straight theta space cos space 3 over 2 straight theta plus 2 space sin space 5 over 2 straight theta space cos space 3 over 2 straight theta plus 2 space sin space 3 over 2 straight theta space cos space 7 over 2 straight theta equals sin space 4 straight theta plus sin space 5 straight theta end style.

Roboguru

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