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Hitunglah hasil dari soal di bawah ini:

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 

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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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 begin mathsize 14px style negative square root of 2 end style.

Pembahasan

Ingat konsep nilai pada kuadran II dan III:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses 180 degree minus alpha close parentheses end cell equals cell negative cos space alpha end cell row cell sin space open parentheses 180 degree minus alpha close parentheses end cell equals cell sin space alpha end cell row cell tan space open parentheses 180 degree minus alpha close parentheses end cell equals cell negative tan space alpha end cell row cell cos space open parentheses 180 degree plus alpha close parentheses end cell equals cell negative cos space alpha end cell end table end style

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 begin mathsize 14px style negative square root of 2 end style.

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