Pertanyaan

Diketahui tan A = 3 2 dan A berada pada kuadaran III, maka tentukan : 3 sin A − cos A cos A + 6 sin A

Diketahui $tan A = \frac{2}{3}$ dan A berada pada kuadaran III, maka tentukan :

$\frac{cos A + 6 sin A}{3 sin A - cos A}$

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

ii,

ii, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cos space straight A plus 6 space sin space straight A over denominator 3 sin space straight A minus cos space straight A end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table$

Pembahasan

Nilai trigonometri pada kuadran III. Dengan teorema pythagoras diperoleh : maka : sehingga diperoleh : Jadiii,

Nilai trigonometri pada kuadran III.

$table attributes columnalign right center left columnspacing 0px end attributes row cell Tan space straight A end cell equals cell fraction numerator sisi space depan space straight A over denominator sisi space samping space straight A end fraction end cell row blank equals cell 2 over 3 end cell end table$

Dengan teorema pythagoras diperoleh :

table attributes columnalign right center left columnspacing 0px end attributes row cell sisi space miring end cell equals cell square root of 2 squared plus 3 squared end root end cell row blank equals cell square root of 4 plus 9 end root end cell row blank equals cell square root of 13 end cell end table

maka :

$table attributes columnalign right center left columnspacing 0px end attributes row cell Cos space straight A end cell equals cell fraction numerator sisi space samping space straight A over denominator sisi space miring end fraction end cell row blank equals cell fraction numerator 3 over denominator square root of 13 end fraction end cell row blank blank cell straight A space left parenthesis ada space di space kuadran space III right parenthesis end cell row cell cos space straight A end cell equals cell negative fraction numerator 3 over denominator square root of 13 end fraction end cell row cell sin space straight A end cell equals cell fraction numerator sisi space depan space straight A over denominator sisi space miring end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 13 end fraction end cell row blank blank cell straight A space left parenthesis space ada space di space kuadran space III stretchy right parenthesis end cell row cell sin space straight A end cell equals cell negative fraction numerator 2 over denominator square root of 13 end fraction end cell end table$

sehingga diperoleh :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cos space straight A plus 6 space sin space straight A over denominator 3 sin space straight A minus cos space straight A end fraction end cell equals cell fraction numerator negative begin display style fraction numerator 3 over denominator square root of 13 end fraction end style plus 6 left parenthesis negative begin display style fraction numerator 2 over denominator square root of 13 end fraction end style right parenthesis over denominator 3 left parenthesis negative begin display style fraction numerator 2 over denominator square root of 13 end fraction end style right parenthesis minus left parenthesis negative begin display style fraction numerator 3 over denominator square root of 13 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator negative 3 minus 12 over denominator square root of 13 end fraction end style over denominator begin display style fraction numerator negative 6 plus 3 over denominator square root of 13 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator negative 15 over denominator square root of 13 end fraction end style over denominator begin display style fraction numerator negative 3 over denominator square root of 13 end fraction end style end fraction end cell row blank equals cell fraction numerator negative 15 over denominator negative 3 end fraction end cell row blank equals 5 end table$

Jadiii, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator cos space straight A plus 6 space sin space straight A over denominator 3 sin space straight A minus cos space straight A end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table$