Kako pretvoriti 9 = (2x + y) ^ 2-3y-x u polarni oblik?

Odgovor:

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

Obrazloženje:

Koristit ćemo:

# 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 / (2 theta 4cos ^ + + 4costhetasintheta 2sin ^ 2 theta-3sintheta-costheta) #

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

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

Kako pretvoriti 9 = (- 2x + y) ^ 2-5y + 3x u polarni oblik?

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 pretvoriti 9x ^ 3-2x-12y ^ 2 = 8 u polarni oblik?

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 ^ 2 theta = 8

Kako pretvoriti 2 = (- x-7y) ^ 2-7x u polarni oblik?

2 = r ^ 2 (costheta + 7sintheta) ^ 2-7rcostheta Koristit ćemo: x = rcostheta y = rsintheta 2 = (- rcostheta-7rsintheta) ^ 2-7rcostheta 2 = (- r) ^ 2 (costheta + 7sintheta) ^ 2-7rcostheta 2 = r ^ 2 (costheta + 7sintheta) ^ 2-7rcostheta Ovo se ne može dalje pojednostavljivati i stoga se mora ostaviti kao implivitna jednadžba.