For the polar graph of r sin 3 a For what values of betwee

For the polar graph of r = sin 3( )

(a) For what values of between 0 and 2 is the graph at the origin?

(b) For what values of between 0 and 2 is the graph farthest from the origin?

Solution

At the origin: r = sin3theta

a) sin3theta =0 ; theta = (pi+2kpi)/3 ; theta= 2kpi/3

theta = 0, pi/3 , pi , 2pi/3

b) farthest from origin : r = sin3theta = 1

sin3theta = 1

theta = (pi +4kpi)/6

theta = pi/6 , 5pi/6, 9pi/6