Pertanyaan

Jika tan α = − 2 1 dan 2 π < α < π ,hitunglah nilai dari: c. tan 4 α

Jika $tan α = - \frac{1}{2}$ dan $\frac{π}{2} < α < π$ , hitunglah nilai dari:

c. $tan 4 α$ $\;$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank tan 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 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank alpha 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 cell 24 over 7 end cell end table

Pembahasan

Sudut Rangkap pada Tangen Pada rumus sudut rangkap, merupakan 2 kali dari . Diketahui dan ,maka letak sudut adalah Pada kuadran II, tangen dan cosinus bernilai negatif sedangkan sinusbernilai positif. Sehingga, adalah: Jadi, .

Sudut Rangkap pada Tangen

$tan space 2 alpha equals fraction numerator 2 space tan space alpha over denominator 1 minus tan squared space alpha end fraction$

Pada rumus sudut rangkap, 2 alpha merupakan 2 kali dari alpha .

Diketahui tan space alpha equals negative 1 half dan straight pi over 2 less than alpha less than straight pi , maka letak sudut alpha adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight pi over 2 end cell less than cell alpha less than straight pi end cell row cell fraction numerator 180 degree over denominator 2 end fraction end cell less than cell alpha less than 180 degree end cell row cell 90 degree end cell less than cell alpha less than 180 degree space open parentheses kuadran space II close parentheses end cell end table$

Pada kuadran II, tangen dan cosinus bernilai negatif sedangkan sinus bernilai positif.

Sehingga, tan space 4 alpha adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space 4 alpha end cell equals cell fraction numerator 2 space tan space 2 alpha over denominator 1 minus tan squared space 2 alpha end fraction end cell row blank equals cell fraction numerator 2 times fraction numerator 2 space tan space alpha over denominator 1 minus tan squared space alpha end fraction over denominator 1 minus open parentheses fraction numerator 2 space tan space alpha over denominator 1 minus tan squared space alpha end fraction close parentheses squared end fraction end cell row blank equals cell fraction numerator fraction numerator 4 times open parentheses negative begin display style 1 half end style close parentheses over denominator 1 minus open parentheses negative 1 half close parentheses squared end fraction over denominator 1 minus open parentheses fraction numerator 2 times open parentheses negative 1 half close parentheses over denominator 1 minus open parentheses negative 1 half close parentheses squared end fraction close parentheses squared end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator negative 2 over denominator 1 minus begin display style 1 fourth end style end fraction end style over denominator 1 minus begin display style open parentheses negative 1 close parentheses squared over open parentheses begin display style 3 over 4 end style close parentheses squared end style end fraction end cell row blank equals cell fraction numerator negative 2 cross times begin display style 4 over 3 end style over denominator 1 minus open parentheses 1 cross times begin display style 16 over 9 end style close parentheses end fraction end cell row blank equals cell fraction numerator negative begin display style 8 over 3 end style over denominator begin display style 9 over 9 end style minus begin display style 16 over 9 end style end fraction end cell row blank equals cell fraction numerator negative begin display style 8 over 3 end style over denominator begin display style negative 7 over 9 end style end fraction end cell row blank equals cell negative fraction numerator 8 over denominator up diagonal strike 3 end fraction cross times open parentheses negative fraction numerator up diagonal strike 9 over denominator 7 end fraction close parentheses end cell row blank equals cell fraction numerator 8 cross times 3 over denominator 7 end fraction end cell row blank equals cell 24 over 7 end cell end table$

Jadi, .