Pertanyaan

Jika tan θ = 3 2 , dimana θ sudut lancip. Hitunglah tanpa menggunakan kalkulator: a. cot 2 θ

Jika $tan θ = \frac{2}{3}$ , dimana $θ$ sudut lancip. Hitunglah tanpa menggunakan kalkulator:

a. $cot 2 θ$

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai .

nilai

cot space 2 straight theta equals 5 over 12

Pembahasan

Ingat kembali: Diketahui , maka: Jadi, nilai .

Ingat kembali:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cot space straight A end cell equals cell fraction numerator 1 over denominator tan space straight A end fraction end cell row cell tan space 2 straight A end cell equals cell fraction numerator 2 space tan space straight A over denominator 1 minus tan squared space straight A end fraction end cell end table$

Diketahui tan space straight theta equals 2 over 3 , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cot space 2 straight theta end cell equals cell fraction numerator 1 over denominator tan space 2 straight theta end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator 2 space tan space straight theta over denominator 1 minus tan squared space straight theta end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator 2 cross times begin display style 2 over 3 end style over denominator 1 minus open parentheses begin display style 2 over 3 end style close parentheses squared end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator begin display style 4 over 3 end style over denominator 1 minus begin display style 4 over 9 end style end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator begin display style 4 over 3 end style over denominator begin display style fraction numerator 9 minus 4 over denominator 9 end fraction end style end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator begin display style 4 over 3 end style over denominator begin display style 5 over 9 end style end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 4 over 3 end style cross times begin display style 9 over 5 end style end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style 36 over 15 end style end fraction end cell row blank equals cell 1 cross times 15 over 36 end cell row blank equals cell 15 over 36 end cell row blank equals cell 5 over 12 end cell end table$

Jadi, nilai cot space 2 straight theta equals 5 over 12 .