Ako konvertujete 2y = y ^ 2-x ^ 2 -4x na polárnu rovnicu?

odpoveď:

#r = - ((2sin (theta) + 4cos (theta)) / cos (2theta)) #

vysvetlenie:

# 2y = y ^ 2-x ^ 2-4x #

# X = rcos (theta) #

# Y = ṛṣīn (theta) #

Zapojte tieto hodnoty do danej rovnice

# 2rsin (theta) = r ^ 2sin ^ 2 (theta) -R ^ 2cos ^ 2 (theta) -4rcos (theta) #

# 2rsin (theta) + 4rcos (theta) = - r ^ 2 (cos ^ 2 (theta) -sin ^ 2 (theta)) #

#r (2sin (theta) + 4cos (theta)) = - r ^ 2 (cos (2theta)) #

Použila sa identita #cos (2theta) = cos ^ 2 (theta) -sin ^ 2 (theta) #

#r = - ((2sin (theta) + 4cos (theta)) / cos (2theta)) #

Ako konvertujete y = 3x ^ 2-5x-y ^ 2 na polárnu rovnicu?

R = - (sintheta + 5costheta) / (sin ^ 2theta-3cos ^ 2theta) Na to potrebujeme nasledovné: 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 ^ 2teta-5costheta rsin ^ 2teta-3rcos ^ 2theta = 2teta-3rcos sintheta-5costheta r = (- sintheta-5costheta) / (sin ^ 2theta-3cos ^ 2theta) = - (sintheta + 5costheta) / (sin ^ 2theta-3cos ^ 2theta)

Ako prepíšem nasledujúcu polárnu rovnicu ako ekvivalentnú karteziánsku rovnicu: r = 5 / (sin (theta) -2cos (theta))?

Y = 2x + 5 r = 5 / (sin (theta) -2cos (theta)) r (sin (theta) -2cos (theta)) = 5 rsin (theta) -2rcos (theta) = 5 Teraz používame nasledovné rovnice: x = rcostheta y = rsintheta Ak chcete získať: y-2x = 5 y = 2x + 5

Ako konvertujete 5y = x -2xy na polárnu rovnicu?

R = (costheta-5sintheta) / (sin (2theta)) Na to použijeme dve rovnice: 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))