Kako grafirate polarno enačbo r = 3 + 3costheta?

Odgovor:

# (x ^ 2 + y ^ 2-3x) ^ 2 = 9x ^ 2 + 9y ^ 2 #

Pojasnilo:

Vsak izraz pomnožite z # r # dobiti:

# r ^ 2 = 3r + 3rcostheta #

# r = sqrt (x ^ 2 + y ^ 2) #

# rcostheta = x #

# x ^ 2 + y ^ 2 = 3sqrt (x ^ 2 + y ^ 2) + 3x #

# (x ^ 2 + y ^ 2-3x) ^ 2 = 9x ^ 2 + 9y ^ 2 #

Kaj je 3costheta v smislu sintete?

3sqrt (1-sin ^ 2 (theta)) Vemo, da cos ^ 2 (theta) + sin ^ 2 (theta) = 1. Torej cos ^ 2 (theta) = 1 - sin ^ 2 (theta) in cos (theta) ) = sqrt (1-sin ^ 2 (theta)). To enakost pomnožimo s 3 in ugotovimo, da 3cos (theta) = 3sqrt (1-sin ^ 2 (theta))