Diketahui sin A=53​, sin B=257​, sudut A lancip dan sudut B tumpul. Nilai cos A cos B−sin A sin B adalah ...

Pertanyaan

Diketahui sin space A equals 3 over 5, sin space B equals 7 over 25, sudut A lancip dan sudut B tumpul. Nilai cos space A space cos space B minus sin space A space sin space B adalah ...

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

nilai 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 A 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 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 B 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 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 A 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 B end table adalah negative 117 over 125 

Pembahasan

Diketahui sin space A equals 3 over 5, artinya fraction numerator sisi space di space depan space angle A over denominator sisi space miring end fraction equals 3 over 5, sehingga melalui Teorema Pythagoras didapatkan sisi sampingnya 4 atau cos space A equals fraction numerator sisi space di space samping space angle A over denominator sisi space miring end fraction equals 4 over 5. Nilai cos space A positif karena A  lancip.

sin space B equals 7 over 25 artinya fraction numerator sisi space di space depan space angle B over denominator sisi space miring end fraction equals 7 over 25, sehingga melalui Teorema Pythagoras didapatkan sisi sampingnya 24 atau cos space B equals fraction numerator sisi space di space samping space angle A over denominator sisi space miring end fraction equals negative 24 over 25. Nilai cos space B negatif, karena B tumpul (nilai trigonometri ada di kuadran II). Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space A space cos space B minus sin space A space sin space B end cell equals cell 4 over 5 cross times open parentheses negative 24 over 25 close parentheses minus 3 over 5 cross times 7 over 25 end cell row blank equals cell negative 96 over 125 minus 21 over 125 end cell row blank equals cell negative 117 over 125 end cell end table

Jadi, nilai 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 A 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 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 B 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 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 A 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 B end table adalah negative 117 over 125 

356

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