Kako pretvorite y = 3x ^ 2-5x-y ^ 2 v polarno enačbo?

Odgovor:

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

Pojasnilo:

Za to potrebujemo naslednje:

# x = rcostheta #

# y = rsintheta #

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

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

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

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

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

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

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

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

Kako pretvorite 5y = x -2xy v polarno enačbo?

R = (costheta-5sintheta) / (sin (2theta)) Za to bomo uporabili dve enačbi: 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))

Pretvorite polarno enačbo v pravokotno enačbo ?! percalc hw pomoč?

D Najprej pomnožite vsako stran z 1-sintheto, da dobite: r-rsintheta = 4/5 r ^ 2 = x ^ 2 + y ^ 2 rsintheta = y sqrt (x ^ 2 + y ^ 2) = 4/5 + yx ^ 2 + y ^ 2 = 16/25 + (8y) / 5 + y ^ 2 x ^ 2 = 16/25 + (8y) / 5 25x ^ 2 = 16 + 40y 25x ^ 2-40y-16 = 0 ne ustreza nobenemu od odgovorov, ki daje, torej