Pertanyaan

Tentukan nilai dari: cot 13 5 ∘ cos 21 0 ∘ csc 31 5 ∘ sin 30 0 ∘ tan 33 0 ∘ sec 42 0 ∘

Tentukan nilai dari:

$\frac{sin 30 0 ^{\circ} tan 33 0 ^{\circ} sec 42 0 ^{\circ}}{cot 13 5 ^{\circ} cos 21 0 ^{\circ} csc 31 5 ^{\circ}}$

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $fraction numerator sin space 300 degree space tan space 330 degree space sec space 420 degree over denominator cot space 135 degree space cos space 210 degree space csc space 315 degree end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 6 over denominator 3 end fraction end cell end table$ .

Pembahasan

Gunakanlah sudut berelasi untuk menjawab soal di atas. Ingat! Nilai sin pada kuadran II adalah positif, sedangkan nilai cos dan tan negatif. Nilai tan pada kuadran III positif, sedangkan nilai sin dan cos negatif. Nilai cos pada kuadran IV positif, sedangkan nilai sin dan tan negatif. Berdasarkan nilai trigonometri pada kuadran II, III, dan IV di atas, maka: Dengan demikian, nilai dari adalah .

Gunakanlah sudut berelasi untuk menjawab soal di atas.

Ingat!

Nilai sin pada kuadran II adalah positif, sedangkan nilai cos dan tan negatif.
Nilai tan pada kuadran III positif, sedangkan nilai sin dan cos negatif.
Nilai cos pada kuadran IV positif, sedangkan nilai sin dan tan negatif.

Berdasarkan nilai trigonometri pada kuadran II, III, dan IV di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space 300 degree space tan space 330 degree space sec space 420 degree over denominator cot space 135 degree space cos space 210 degree space csc space 315 degree end fraction end cell equals cell fraction numerator sin space 300 degree space tan space 330 degree space begin display style fraction numerator 1 over denominator cos space 420 degree end fraction end style over denominator begin display style fraction numerator 1 over denominator tan space 135 degree end fraction end style space cos space 210 degree space begin display style fraction numerator 1 over denominator sin space 315 degree end fraction end style end fraction end cell row blank equals cell fraction numerator sin space 300 degree space tan space 330 degree space tan space 135 degree space sin space 315 degree over denominator begin display style cos space 210 degree space cos space 420 degree end style end fraction end cell row blank equals cell fraction numerator sin open parentheses 360 degree minus 60 degree close parentheses times tan open parentheses 360 degree minus 30 degree close parentheses times begin display style tan open parentheses 180 degree minus 45 degree close parentheses times sin open parentheses 360 degree minus 45 degree close parentheses end style over denominator begin display style cos open parentheses 1 times 360 degree plus 60 degree close parentheses end style times cos open parentheses 180 degree plus 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative sin space 60 degree times open parentheses negative tan space 30 degree close parentheses times open parentheses negative tan space 45 degree close parentheses times open parentheses negative sin space 45 degree close parentheses over denominator cos space 60 degree times open parentheses negative cos space 30 degree close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator square root of 3 over denominator 2 end fraction end style times open parentheses negative begin display style fraction numerator square root of 3 over denominator 3 end fraction end style close parentheses times open parentheses negative 1 close parentheses times open parentheses negative begin display style fraction numerator square root of 2 over denominator 2 end fraction end style close parentheses over denominator begin display style 1 half end style times open parentheses negative begin display style fraction numerator square root of 3 over denominator 2 end fraction end style close parentheses end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 3 square root of 2 over denominator 4 times 3 end fraction end style over denominator negative begin display style fraction numerator square root of 3 over denominator 4 end fraction end style end fraction end cell row blank equals cell negative fraction numerator square root of 2 over denominator 4 end fraction times fraction numerator 4 over denominator square root of 3 end fraction end cell row blank equals cell negative fraction numerator square root of 2 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell negative fraction numerator square root of 6 over denominator 3 end fraction. end cell end table$

Dengan demikian, nilai dari $fraction numerator sin space 300 degree space tan space 330 degree space sec space 420 degree over denominator cot space 135 degree space cos space 210 degree space csc space 315 degree end fraction$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator square root of 6 over denominator 3 end fraction end cell end table$ .