Hitunglah hasil dari soal di bawah ini: sin150∘⋅cos225∘sin45∘⋅cos135∘⋅tan135∘

Hitunglah hasil dari soal di bawah ini: sin150∘⋅c...

Pertanyaan

Hitunglah hasil dari soal di bawah ini:

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai dari $begin mathsize 14px style fraction numerator sin space 45 degree times cos space 135 degree times tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction end style$ adalah

Pembahasan

Ingat konsep nilai pada kuadran II dan III:

Kemudian gunakan konsep tersebut sehingga:

$begin mathsize 14px style fraction numerator sin space 45 degree times cos space 135 degree times tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction equals fraction numerator sin space 45 degree times cos space open parentheses 180 degree minus 45 degree close parentheses times tan space open parentheses 180 degree minus 45 degree close parentheses over denominator sin space open parentheses 180 degree minus 30 degree close parentheses times cos space open parentheses 180 degree plus 45 degree close parentheses end fraction equals fraction numerator sin space 45 degree times open parentheses negative cos space 45 degree close parentheses times open parentheses negative tan space 45 degree close parentheses over denominator open parentheses sin space 30 degree close parentheses times open parentheses negative cos space 45 degree close parentheses end fraction equals fraction numerator begin display style 1 half end style square root of 2 times open parentheses negative 1 half square root of 2 close parentheses times open parentheses negative 1 close parentheses over denominator open parentheses begin display style 1 half end style close parentheses open parentheses negative begin display style 1 half end style square root of 2 close parentheses end fraction equals fraction numerator begin display style 1 fourth end style times 2 over denominator negative begin display style 1 fourth end style square root of 2 end fraction equals negative fraction numerator 2 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals negative square root of 2 end style$

Dengan demikian nilai dari $begin mathsize 14px style fraction numerator sin space 45 degree times cos space 135 degree times tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction end style$ adalah .