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13. Hitunglah tanpa menggunakan kalkulator atau tabel trigonometri. c. sin 15∘−sin 75∘cos 15∘−cos 75∘​

Pertanyaan

13. Hitunglah tanpa menggunakan kalkulator atau tabel trigonometri.

c. fraction numerator cos space 15 degree minus cos space 75 degree over denominator sin space 15 degree minus sin space 75 degree end fraction  

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

 table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator size 12px cos size 12px space size 12px 15 size 12px degree size 12px minus size 12px cos size 12px space size 12px 75 size 12px degree over denominator size 12px sin size 12px space size 12px 15 size 12px degree size 12px minus size 12px sin size 12px space size 12px 75 size 12px degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 12px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 12px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 12px 1 end table.

Pembahasan

Ingat rumus identitas selisih sinus dan selisih cosinus berikut:

  • sin space x minus sin space y equals 2 space cos space 1 half open parentheses x plus y close parentheses space sin space 1 half open parentheses x minus y close parentheses 
  • cos space x minus cos space y equals negative 2 space sin space 1 half open parentheses x plus y close parentheses space sin space 1 half open parentheses x minus y close parentheses 

Dari soal diketahui:

x15 degree 

y = 75 degree 

Sehingga persamaan trigonometri tersebut menjadi:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space 15 degree minus cos space 75 degree over denominator sin space 15 degree minus sin space 75 degree end fraction end cell equals cell fraction numerator negative 2 space sin space 1 half open parentheses 15 degree plus 75 degree close parentheses space sin space 1 half open parentheses 15 degree minus 75 degree close parentheses over denominator 2 space cos space 1 half open parentheses 15 degree plus 75 degree close parentheses space sin space 1 half open parentheses 15 degree minus 75 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative 2 space sin space 1 half open parentheses 90 degree close parentheses space sin space 1 half open parentheses negative 60 degree close parentheses over denominator 2 space cos space 1 half open parentheses 90 degree close parentheses space sin space 1 half open parentheses negative 60 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative 2 space sin space open parentheses 45 degree close parentheses space up diagonal strike sin space open parentheses negative 30 degree close parentheses end strike over denominator 2 space cos space open parentheses 45 degree close parentheses space up diagonal strike sin space open parentheses negative 30 degree close parentheses end strike end fraction end cell row blank equals cell fraction numerator negative 2 open parentheses begin display style 1 half end style square root of 2 close parentheses over denominator 2 open parentheses begin display style 1 half end style square root of 2 close parentheses end fraction end cell row blank equals cell negative 1 end cell end table end style 

Dengan demikian, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator size 12px cos size 12px space size 12px 15 size 12px degree size 12px minus size 12px cos size 12px space size 12px 75 size 12px degree over denominator size 12px sin size 12px space size 12px 15 size 12px degree size 12px minus size 12px sin size 12px space size 12px 75 size 12px degree end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank size 12px equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 12px minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank size 12px 1 end table.

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