Pertanyaan

Jika sin x = a dan cos y = b dengan 0 < x < 2 π , dan 2 π < y < π , maka hitung tan x + tan y

Jika $sin x = a$ dan $cos y = b$ dengan $0 < x < \frac{π}{2}$ , dan $\frac{π}{2} < y < π$ , maka hitung $tan x + tan y$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

nilai .

nilai $table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x plus tan y end cell equals cell fraction numerator a square root of 1 minus a squared end root over denominator open parentheses 1 minus a squared close parentheses end fraction plus fraction numerator square root of 1 minus b squared end root over denominator b end fraction end cell end table$ .

Pembahasan

Untuk Didapat Untuk (dengan karena y berada di kuadran II) Didapat Sehingga: . Jadi nilai .

Untuk sin space x equals a over 1 equals de over mi

table attributes columnalign right center left columnspacing 0px end attributes row sa equals cell square root of mi squared minus de squared end root end cell row blank equals cell square root of 1 squared minus a squared end root end cell row blank equals cell square root of 1 minus a squared end root end cell end table

Didapat

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x end cell equals cell de over sa end cell row blank equals cell fraction numerator a over denominator square root of 1 minus a squared end root end fraction cross times fraction numerator square root of 1 minus a squared end root over denominator square root of 1 minus a squared end root end fraction end cell row blank equals cell fraction numerator a square root of 1 minus a squared end root over denominator 1 minus a squared end fraction end cell end table$

Untuk cos space y space equals b over 1 equals sa over mi (dengan b less than 0 karena y berada di kuadran II)

Didapat

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space y end cell equals cell de over sa end cell row blank equals cell fraction numerator square root of 1 minus b squared end root over denominator b end fraction end cell end table$

Sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x plus tan y end cell equals cell fraction numerator a square root of 1 minus a squared end root over denominator open parentheses 1 minus a squared close parentheses end fraction plus fraction numerator square root of 1 minus b squared end root over denominator b end fraction end cell end table$ .

Jadi nilai $table attributes columnalign right center left columnspacing 0px end attributes row cell tan space x plus tan y end cell equals cell fraction numerator a square root of 1 minus a squared end root over denominator open parentheses 1 minus a squared close parentheses end fraction plus fraction numerator square root of 1 minus b squared end root over denominator b end fraction end cell end table$ .