Odgovor:
Pojasnilo:
Za to bomo uporabili dve enačbi:
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)
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
Kako pretvorite y = -y ^ 2-3x ^ 2-xy v polarno enačbo?
R = - (sintheta) / (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) Ponovno napišite kot: y ^ 2 + 3x ^ 2 + xy = -y Namestitev: x = rcostheta y = rsintheta (rsintheta) ^ 2 + 3 ( rcostheta) ^ 2 + (rcostheta) (rsintheta) = - rsintheta r ^ 2 (sintheta) ^ 2 + 3r ^ 2 (costheta) ^ 2 + r ^ 2 (costhetasintheta) = - rsintheta Razdelite obe strani z rr (sintheta) ^ 2 + 3r (costheta) ^ 2 + r (costhetasintheta) = - sintheta Faktoriziraj r: r (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) = - sintheta Naredi r predmet: r = - (sintheta) / (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta)