Bagaimana anda menukar y = -y ^ 2-3x ^ 2-xy ke dalam persamaan kutub?

Jawapan:

#r = - (sintheta) / (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) #

Penjelasan:

Tulis semula sebagai:

# y ^ 2 + 3x ^ 2 + xy = -y #

Pengganti dalam:

# x = rcostheta #

# y = rsintheta #

# (rsintheta) ^ 2 + 3 (rcostheta) ^ 2 + (rcostheta) (rsintheta) = - rsintheta #

# r ^ 2 (sintheta) ^ 2 + 3r ^ 2 (costheta) ^ 2 + r ^ 2 (costhetasintheta) = - rsintheta #

Bahagikan kedua belah pihak # r #

#r (sintheta) ^ 2 + 3r (costheta) ^ 2 + r (costhetasintheta) = - sintheta #

Faktor kesilapan # r #:

#r (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) = - sintheta #

Buat # r # subjek:

#r = - (sintheta) / (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) #

Bagaimana anda menukar 9 = (- 2x + y) ^ 2-5y + 3x ke dalam bentuk kutub?

9 = 4r ^ 2cos ^ 2 (theta) -4r ^ 2sinthetacostheta + r ^ 2sin ^ 2 (theta) -5rsintheta + 3rcostheta = r (sintheta (r (sintheta-4costheta) -5) + costheta (4rcostheta + 3) = rcostheta y = rsintheta 9 = (- 2 (rcostheta) + rsintheta) ^ 2-5rsintheta + 3rcostheta 9 = 4r ^ 2cos ^ 2 (theta) -4r ^ 2sinthetacostheta + r ^ 2sin ^ 2 (theta) -5rsintheta + = r (sintheta (r (sintheta-4costheta) -5) + costheta (4rcostheta + 3))

Bagaimana anda menukar 9 = (2x + y) ^ 2-3y-x ke dalam bentuk kutub?

Kita akan menggunakan: x = rcostheta y = rsintheta 9 = (2rcostheta + rsintheta) ^ 2-3rsintheta-rcostheta 9 = r ( R = 9 / (2costheta + sintheta) ^ 2-3sintheta-costheta) r = 9 / (4cos ^ 2theta + 4costhetasintheta + 2sin ^ 2theta-3sintheta-costheta) r = 9 / (2 (2cos ^ 2theta + sin ^ 2theta) + 2sin (2theta) -3sintheta-costheta) r = 9 / (2 (cos ^ 2theta + 1) + 2sin (2theta)

Bagaimana anda menukar 5y = x -2xy ke dalam persamaan kutub?

R = (costheta-5sintheta) / (sin (2theta)) Untuk ini kita akan menggunakan dua persamaan: x = rcostheta, y = rsintheta 5rsintheta = rcostheta-2 (rcos theta) (rsintheta) 5rsintheta = rcostheta-2r ^ 2costhetasintheta 5sintheta = costheta-2rcosthetasintheta 2rcosthetasintheta = costheta-5sintheta r = (costheta-5sintheta) / (2costhetasintheta) r = (costheta-5sintheta) / (sin (2theta))