Pertanyaan

Diketahui sin 3 0 ∘ = h dan cos 4 0 ∘ = k . Nyatakan pernyataan berikut dalam h dan/atau k . a. sin 7 0 ∘

Diketahui $sin 3 0^{\circ} = h$ dan $cos 4 0^{\circ} = k$ . Nyatakan pernyataan berikut dalam $h$ dan/atau $k$ .

a. $sin 7 0^{\circ}$

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai .

nilai

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 equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank h end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank k 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 cell square root of 1 minus k squared minus h squared minus h squared k squared end root end cell end table

Pembahasan

Ingat kembali: Diketahui dan , maka: - Menentukan nilai Berarti: - Menentukan nilai Berarti: Sehingga: Jadi, nilai .

Ingat kembali:

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight A end cell equals cell fraction numerator sisi space depan over denominator sisi space miring end fraction end cell row cell cos space straight A end cell equals cell fraction numerator sisi space samping over denominator sisi space miring end fraction end cell row cell sin space open parentheses straight A plus straight B close parentheses end cell equals cell sin space straight A times cos space straight B plus cos space straight A times sin space straight B end cell end table$

Diketahui sin space 30 degree equals h dan cos space 40 degree equals k , maka:

- Menentukan nilai cos space 30 degree

$sin space 30 degree equals h sin space 30 degree equals h over 1 rightwards arrow fraction numerator sisi space depan over denominator sisi space miring end fraction$

Berarti:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 30 degree end cell equals cell fraction numerator sisi space samping over denominator sisi space miring end fraction end cell row blank equals cell fraction numerator square root of 1 squared minus h squared end root over denominator 1 end fraction end cell row blank equals cell fraction numerator square root of 1 minus h squared end root over denominator 1 end fraction end cell row blank equals cell square root of 1 minus h squared end root end cell end table$

- Menentukan nilai sin space 40 degree

$cos space 40 degree equals k cos space 40 degree equals k over 1 rightwards arrow fraction numerator sisi space samping over denominator sisi space miring end fraction$

Berarti:

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 40 degree end cell equals cell fraction numerator sisi space depan over denominator sisi space miring end fraction end cell row blank equals cell fraction numerator square root of 1 squared minus k squared end root over denominator 1 end fraction end cell row blank equals cell fraction numerator square root of 1 minus k squared end root over denominator 1 end fraction end cell row blank equals cell square root of 1 minus k squared end root end cell end table$

Sehingga:

Jadi, nilai .