Kako pretvoriti 2y = y ^ 2-x ^ 2 -4x u polarnu jednadžbu?

Odgovor:

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

Obrazloženje:

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

# x = rcos (theta) #

# Y = rsin (theta) #

Uključite ove vrijednosti u danu jednadžbu

# 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)) #

Koristio je identitet #cos (2 theta) = cos ^ 2 (theta) -sin ^ 2 (theta) #

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

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

R = - (sintheta + 5costheta) / (sin ^ 2theta-3cos ^ 2theta) Za to nam je potrebno sljedeće: 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 sintheta-5costheta r = (- sintheta-5costheta) / (sin ^ 2theta-3cos ^ 2theta) = - (sintheta + 5costheta) / (sin ^ 2theta-3cos ^ 2theta)

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))