Transform to Cartesian coordinate the equations
`r^(1/3) = a^(1/2) sin (theta)/(2)`.

Transform to Cartesian coordinates the equations: r^(2)=a^(2)cos2 theta

The Cartesian coordinates of a point (-1,(3 pi)/(4)) are

The solution of the equation 1-"cos" theta = "sin" theta "sin" (theta)/(2) is

Convert into Cartesian coordinates: ((sqrt2+1)/sqrt2,pi/4)

Convert Cartesian coordinate into polar coordinate (1, -sqrt3)

Convert Cartesian coordinate into polar coordinate (-1, sqrt3)

The most general value of theta satisfying both the equations sin theta=(1)/(2):tan theta=(1)/(sqrt(3)) is