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Diketahui  dan . Jika  lancip, maka nilai dari

Pertanyaan

Diketahui sin space italic A equals 12 over 13 dan cos space B equals 3 over 5. Jika angle italic A italic space dan italic space angle B lancip, maka nilai dari tan space left parenthesis italic A minus sign B right parenthesis equals.... 

Pembahasan Soal:

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space A end cell equals cell 12 over 13 end cell row cell cos space B end cell equals cell 3 over 5 end cell end table 

Karena table attributes columnalign right center left columnspacing 0px end attributes row blank blank angle end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank A 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 dan 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 angle end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank B 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 lancip end table maka kedua sudut tersebut ada di kuadran I sehingga nilai fungsi trigonometrinya selalu positif. Selanjutnya dapat ditentukan cos space italic A space dan space sin space B dengan identitas trigonometri sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row 1 equals cell sin squared space italic A plus cos squared space italic A end cell row cell cos italic space italic A end cell equals cell square root of 1 minus sign sin squared space italic A end root end cell row blank equals cell square root of 1 minus sign begin italic style left parenthesis straight 12 over straight 13 right parenthesis end style squared end root end cell row blank equals cell square root of 1 minus sign 144 over 169 end root end cell row blank equals cell square root of fraction numerator 169 minus sign 144 over denominator 169 end fraction end root end cell row blank equals cell square root of 25 over 169 end root end cell row blank equals cell 5 over 13 end cell row blank blank blank row 1 equals cell sin squared space B plus cos squared space B end cell row cell sin italic space B end cell equals cell square root of 1 minus sign cos squared space B end root end cell row blank equals cell square root of 1 minus sign begin italic style left parenthesis 3 over 5 right parenthesis end style squared end root end cell row blank equals cell square root of 1 minus sign 9 over 25 end root end cell row blank equals cell square root of fraction numerator 25 minus sign 9 over denominator 25 end fraction end root end cell row blank equals cell square root of 16 over 25 end root end cell row blank equals cell 4 over 5 end cell end table 

Sehingga dapat ditentukan nilai dari tan space left parenthesis italic A minus sign B right parenthesis sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space open parentheses italic A minus sign B close parentheses end cell equals cell fraction numerator sin space left parenthesis italic A minus sign B right parenthesis over denominator cos space left parenthesis italic A minus sign B right parenthesis end fraction end cell row blank equals cell fraction numerator sin space italic A space cos space B bond sin space B space cos space italic A over denominator cos space italic A space cos space B and sin space italic A space sin space B end fraction end cell row blank equals cell fraction numerator open parentheses begin display style 12 over 13 end style close parentheses middle dot open parentheses begin display style 3 over 5 end style close parentheses minus sign open parentheses begin display style 4 over 5 end style close parentheses middle dot open parentheses begin display style 5 over 13 end style close parentheses over denominator open parentheses begin display style 5 over 13 end style close parentheses middle dot open parentheses begin display style 3 over 5 end style close parentheses plus open parentheses begin display style 12 over 13 end style close parentheses middle dot open parentheses begin display style 4 over 5 end style close parentheses end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 36 minus sign 20 over denominator up diagonal strike 65 end fraction end style over denominator begin display style fraction numerator 15 plus 48 over denominator up diagonal strike 65 end fraction end style end fraction end cell row blank equals cell 16 over 63 end cell end table 

Dengan demikian nilai dari tan space left parenthesis A minus B right parenthesis equals 16 over 63.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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