Trigonometri Contoh

Sederhanakan (cos(y)+1/y*sin(x)-1/y*sin(y))/(1/y*cos(x)+xcos(y)-x/y*sin(y))
cos(y)+1ysin(x)-1ysin(y)1ycos(x)+xcos(y)-xysin(y)cos(y)+1ysin(x)1ysin(y)1ycos(x)+xcos(y)xysin(y)
Langkah 1
Sederhanakan pembilangnya.
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Langkah 1.1
Gabungkan 1y1y dan sin(x)sin(x).
cos(y)+sin(x)y-1ysin(y)1ycos(x)+xcos(y)-xysin(y)cos(y)+sin(x)y1ysin(y)1ycos(x)+xcos(y)xysin(y)
Langkah 1.2
Gabungkan sin(y)sin(y) dan 1y1y.
cos(y)+sin(x)y-sin(y)y1ycos(x)+xcos(y)-xysin(y)cos(y)+sin(x)ysin(y)y1ycos(x)+xcos(y)xysin(y)
cos(y)+sin(x)y-sin(y)y1ycos(x)+xcos(y)-xysin(y)cos(y)+sin(x)ysin(y)y1ycos(x)+xcos(y)xysin(y)
Langkah 2
Sederhanakan penyebutnya.
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Langkah 2.1
Gabungkan 1y1y dan cos(x)cos(x).
cos(y)+sin(x)y-sin(y)ycos(x)y+xcos(y)-xysin(y)cos(y)+sin(x)ysin(y)ycos(x)y+xcos(y)xysin(y)
Langkah 2.2
Gabungkan sin(y)sin(y) dan xyxy.
cos(y)+sin(x)y-sin(y)ycos(x)y+xcos(y)-sin(y)xycos(y)+sin(x)ysin(y)ycos(x)y+xcos(y)sin(y)xy
cos(y)+sin(x)y-sin(y)ycos(x)y+xcos(y)-sin(y)xycos(y)+sin(x)ysin(y)ycos(x)y+xcos(y)sin(y)xy
Langkah 3
Multiply the numerator and denominator of the fraction by yy.
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Langkah 3.1
Kalikan cos(y)+sin(x)y-sin(y)ycos(x)y+xcos(y)-sin(y)xycos(y)+sin(x)ysin(y)ycos(x)y+xcos(y)sin(y)xy dengan yyyy.
yycos(y)+sin(x)y-sin(y)ycos(x)y+xcos(y)-sin(y)xyyycos(y)+sin(x)ysin(y)ycos(x)y+xcos(y)sin(y)xy
Langkah 3.2
Gabungkan.
y(cos(y)+sin(x)y-sin(y)y)y(cos(x)y+xcos(y)-sin(y)xy)y(cos(y)+sin(x)ysin(y)y)y(cos(x)y+xcos(y)sin(y)xy)
y(cos(y)+sin(x)y-sin(y)y)y(cos(x)y+xcos(y)-sin(y)xy)y(cos(y)+sin(x)ysin(y)y)y(cos(x)y+xcos(y)sin(y)xy)
Langkah 4
Terapkan sifat distributif.
ycos(y)+ysin(x)y+y(-sin(y)y)ycos(x)y+y(xcos(y))+y(-sin(y)xy)ycos(y)+ysin(x)y+y(sin(y)y)ycos(x)y+y(xcos(y))+y(sin(y)xy)
Langkah 5
Sederhanakan dengan cara membatalkan .
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Langkah 5.1
Batalkan faktor persekutuan dari yy.
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Langkah 5.1.1
Batalkan faktor persekutuan.
ycos(y)+ysin(x)y+y(-sin(y)y)ycos(x)y+y(xcos(y))+y(-sin(y)xy)
Langkah 5.1.2
Tulis kembali pernyataannya.
ycos(y)+sin(x)+y(-sin(y)y)ycos(x)y+y(xcos(y))+y(-sin(y)xy)
ycos(y)+sin(x)+y(-sin(y)y)ycos(x)y+y(xcos(y))+y(-sin(y)xy)
Langkah 5.2
Batalkan faktor persekutuan dari y.
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Langkah 5.2.1
Pindahkan negatif pertama pada -sin(y)y ke dalam pembilangnya.
ycos(y)+sin(x)+y-sin(y)yycos(x)y+y(xcos(y))+y(-sin(y)xy)
Langkah 5.2.2
Batalkan faktor persekutuan.
ycos(y)+sin(x)+y-sin(y)yycos(x)y+y(xcos(y))+y(-sin(y)xy)
Langkah 5.2.3
Tulis kembali pernyataannya.
ycos(y)+sin(x)-sin(y)ycos(x)y+y(xcos(y))+y(-sin(y)xy)
ycos(y)+sin(x)-sin(y)ycos(x)y+y(xcos(y))+y(-sin(y)xy)
Langkah 5.3
Batalkan faktor persekutuan dari y.
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Langkah 5.3.1
Batalkan faktor persekutuan.
ycos(y)+sin(x)-sin(y)ycos(x)y+y(xcos(y))+y(-sin(y)xy)
Langkah 5.3.2
Tulis kembali pernyataannya.
ycos(y)+sin(x)-sin(y)cos(x)+y(xcos(y))+y(-sin(y)xy)
ycos(y)+sin(x)-sin(y)cos(x)+y(xcos(y))+y(-sin(y)xy)
Langkah 5.4
Batalkan faktor persekutuan dari y.
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Langkah 5.4.1
Pindahkan negatif pertama pada -sin(y)xy ke dalam pembilangnya.
ycos(y)+sin(x)-sin(y)cos(x)+y(xcos(y))+y-sin(y)xy
Langkah 5.4.2
Batalkan faktor persekutuan.
ycos(y)+sin(x)-sin(y)cos(x)+y(xcos(y))+y-sin(y)xy
Langkah 5.4.3
Tulis kembali pernyataannya.
ycos(y)+sin(x)-sin(y)cos(x)+y(xcos(y))-sin(y)x
ycos(y)+sin(x)-sin(y)cos(x)+y(xcos(y))-sin(y)x
ycos(y)+sin(x)-sin(y)cos(x)+y(xcos(y))-sin(y)x
Langkah 6
Susun kembali faktor-faktor dalam ycos(y)+sin(x)-sin(y)cos(x)+y(xcos(y))-sin(y)x.
ycos(y)+sin(x)-sin(y)cos(x)+yxcos(y)-xsin(y)
 [x2  12  π  xdx ]