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

Pertanyaan

Jika  dan  dengan , dan , maka hitung  

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

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

Pembahasan

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)

table attributes columnalign right center left columnspacing 0px end attributes row cell de squared end cell equals cell mi squared minus sa squared end cell row blank equals cell plus-or-minus square root of 1 squared minus b squared end root end cell row blank equals cell square root of 1 minus b squared end root space left parenthesis de space greater than 0 comma space karena space di space kuadran space II right parenthesis end cell end table 

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.

137

5.0 (7 rating)

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Diketahui sudut A berada di kuadran I dan sudut B berada di kuadran II. Jika cos A=43​ dan cos B=−52​, berapakah nilai sin A+sin B?

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Jawaban terverifikasi

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