Kako pretvoriti y = 3x ^ 2-5x-y ^ 2 u polarnu jednadžbu?

Odgovor:

#R = - (+ sintheta 5costheta) / (sin ^ 2 theta-3cos ^ 2 theta) #

Obrazloženje:

Za to nam je potrebno sljedeće:

# x = rcostheta #

# Y = rsintheta #

# Rsintheta = 3 (rcostheta) ^ 2-5 (rcostheta) - (rsintheta) ^ 2 #

# Rsintheta = 3r ^ 2cos ^ 2 theta-5rcostheta-r ^ 2sin ^ 2 theta #

# Rsintheta + R ^ 2sin ^ 2 theta = 3r ^ 2cos ^ 2 theta-5rcostheta #

# Sintheta + rsin ^ 2 theta = 3rcos ^ 2 theta-5costheta #

# rsin ^ 2 theta-3rcos ^ 2 theta = -sintheta-5costheta #

#R = (- sintheta-5costheta) / (sin ^ 2 theta-3cos ^ 2 theta) = - (+ sintheta 5costheta) / (sin ^ 2 theta-3cos ^ 2 theta) #

Kako pretvoriti y = 2y ^ 2 + 3x ^ 2-2xy u polarnu jednadžbu?

R = sintheta / (2sin ^ 2theta + 3cos ^ 2theta-sin (2theta)) Za to će nam trebati: x = rcostheta y = rsintheta rsintheta = 2 (rsintheta) ^ 2 + 3 (rcostheta) ^ 2-2 (rcostheta) (rsintheta) rsintheta = 2r ^ 2sin ^ 2theta + 3r ^ 2cos ^ 2theta-2r ^ 2costhetasintheta sintheta = 2rsin ^ 2theta + 3rcos ^ 2theta-2rcosthetasintheta sintheta = 2rsin ^ 2tea + 3rcos ^ 2 theta + 3cos ^ 2theta-sin (2theta)) r = sinteta / (2sin ^ 2theta + 3cos ^ 2theta-sin (2theta))

Kako pretvoriti 5y = x -2xy u polarnu jednadžbu?

R = (costheta-5sintheta) / (sin (2theta)) Za ovo ćemo koristiti dvije jednadžbe: 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))

Kako pretvoriti y = -y ^ 2-3x ^ 2-xy u polarnu jednadžbu?

R = - (sintheta) / (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) Prepisati kao: y ^ 2 + 3x ^ 2 + xy = -y Zamijeniti u: x = rcostheta y = rsintheta (rsintheta) ^ 2 + 3 ( rcostheta) ^ 2 + (rcostheta) (rsintheta) = - rsintheta r ^ 2 (sinteta) ^ 2 + 3r ^ 2 (costheta) ^ 2 + r ^ 2 (costhetasintheta) = - rsintheta Podijelite obje strane pomoću rr (sintheta) ^ 2 + 3r (costheta) ^ 2 + r (costhetasintheta) = - sintheta Faktoriziranje r: r (sin ^ 2ta + 3cos ^ 2theta + costhetasintheta) = - sintheta Izraditi r subjekt: r = - (sintheta) / (sin ^ 2 theta + 3cos ^ 2 theta + costhetasintheta)