Kako pretvorite y = 2y ^ 2 + 3x ^ 2-2xy v polarno enačbo?

Odgovor:

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

Pojasnilo:

Za to bomo potrebovali:

# 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 ^ 2theta + 3rcos ^ 2theta-rsin (2theta) #

# sintheta = r (2sin ^ 2theta + 3cos ^ 2theta-sin (2theta)) #

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