Vastaus:
# R ^ 2 = 4 / (cos ^ 2theta + 4sin ^ 2theta) #
# R = sqrt (4 / (cos ^ 2theta + 4sin ^ 2theta)) = 2 / sqrt (cos ^ 2theta + 4sin ^ 2theta) #
Selitys:
Käytämme kahta kaavaa:
# X = rcostheta #
# Y = rsintheta #
# X ^ 2 = r ^ 2cos ^ 2theta #
# Y ^ 2 = r ^ 2sin ^ 2theta #
# R ^ 2cos ^ 2theta + 4r ^ 2sin ^ 2theta = 4 #
# R ^ 2 (cos ^ 2theta + 4sin ^ 2theta) = 4 #
# R ^ 2 = 4 / (cos ^ 2theta + 4sin ^ 2theta) #
# R = sqrt (4 / (cos ^ 2theta + 4sin ^ 2theta)) = 2 / sqrt (cos ^ 2theta + 4sin ^ 2theta) #