Kako pretvorite (6, 6) v polarno obliko?

Odgovor:

Izkoristite nekaj formul, ki jih boste dobili # (6,6) -> (6sqrt (2), pi / 4) #.

Pojasnilo:

Želeno pretvorbo iz # (x, y) -> (r, theta) # doseči z uporabo naslednjih formul:

# r = sqrt (x ^ 2 + y ^ 2) #

# theta = tan ^ (- 1) (y / x) #

Z uporabo teh formul dobimo:

# r = sqrt ((6) ^ 2 + (6) ^ 2) = sqrt (72) = 6sqrt (2) #

# theta = tan ^ (- 1) (6/6) = tan ^ (- 1) 1 = pi / 4 #

Tako #(6,6)# v pravokotnih koordinatah ustreza # (6sqrt (2), pi / 4) # v polarnih koordinatah.

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.