Kako pretvorite 2y = y ^ 2-x ^ 2 -4x v polarno enačbo?

Odgovor:

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

Pojasnilo:

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

# x = rcos (theta) #

# y = rsin (theta) #

Te vrednosti vključite v dano enačbo

# 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)) #

Uporabil je identiteto #cos (2theta) = cos ^ 2 (theta) -sin ^ 2 (theta) #

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

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

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

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