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

Jawapan:

# r = (costheta-5sintheta) / (sin (2theta)) #

Penjelasan:

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)) #

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

R = - (sintheta) / (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) Tulis semula sebagai: y ^ 2 + 3x ^ 2 + xy = -y Pengganti dalam: x = rcostheta y = rsintheta (rsintheta) ^ 2 + rcostheta) ^ 2 + (rcostheta) (rsintheta) = - rsintheta r ^ 2 (sintheta) ^ 2 + 3r ^ 2 (costheta) ^ 2 + r ^ 2 (costhetasintheta) = - rsintheta Divide both sides by rr (sintheta) = + Sintetika Faktor r: r (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) = - sintheta Membuat r subjek: r = - (sintheta) / (sin ^ 2orang + 3cos ^ 2theta + costhetasintheta)