Kako pretvorite 9 = (2x + y) ^ 2-3y-x v polarno obliko?

Odgovor:

# r = 9 / (2 (cos ^ 2theta + 1) + 2sin (2theta) -3sintheta-costheta) #

Pojasnilo:

Uporabili bomo:

# x = rcostheta #

# y = rsintheta #

# 9 = (2rcostheta + rsintheta) ^ 2-3rsintheta-rcostheta #

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

# 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) -3sintheta-costheta) #

Kako pretvorite 9 = (- 2x + y) ^ 2-5y + 3x v polarno obliko?

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

Kako pretvorite 9x ^ 3-2x-12y ^ 2 = 8 v polarno obliko?

9r ^ 3cos ^ 3theta-2rcostheta-12r ^ 2sin ^ 2theta = 8 x = rcostheta y = rsintheta 9 (rcostheta) ^ 3-2 (rcostheta) -12 (rsintheta) ^ 2 = 8 9r ^ 3cos ^ 3theta-2rcostheta-12r ^ 2sin ^ 2theta = 8

Kako pretvorite 2 = (- x-7y) ^ 2-7x v polarno obliko?

2 = r ^ 2 (costheta + 7sintheta) ^ 2-7rcostheta Uporabili bomo: x = rcostheta y = rsintheta 2 = (- rcostheta-7rsintheta) ^ 2-7rcostheta 2 = (- r) ^ 2 (costheta + 7sintheta) ^ 2-7rcostheta 2 = r ^ 2 (costheta + 7sintheta) ^ 2-7rcostheta Tega ne moremo več poenostaviti in jo moramo pustiti kot enačbo za implivit.