Hvordan konverterer du 2y = y ^ 2-x ^ 2 -4x til en polarligning?

Svar:

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

Forklaring:

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

# x = rcos (theta) #

# Y = rsin (theta) #

Plugg disse verdiene i den gitte ligningen

# 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)) #

Brukt identiteten #cos (2teta) = cos ^ 2 (theta) -sin ^ 2 (theta) #

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

Hvordan konverterer du y = 3x ^ 2-5x-y ^ 2 til en polarligning?

R = - (sintheta + 5costheta) / (sin ^ 2theta-3cos ^ 2theta) For dette trenger vi følgende: 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 ^ 2ta-3cos ^ 2theta) = - (sintheta + 5costheta) /

Hvordan konverterer du y = 2y ^ 2 + 3x ^ 2-2xy til en polarligning?

For dette vil vi trenge: x = rcostheta y = rsintheta rsintheta = 2 (rsintheta) ^ 2 + 3 (rcostheta) ^ 2-2 (rcostheta) ^ 2-2 (rcostheta) (rsintheta) rsintheta = 2r ^ 2sin ^ 2teta + 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 ^ 2ta + 3cos ^ 2theta-sin (2theta))

Hvordan konverterer du 5y = x -2xy til en polarligning?

R = (costheta-5sintheta) / (sin (2theta)) For dette vil vi bruke de to ligningene: 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))