How do you find the points of intersection of #r=4-5sintheta, r=3sintheta#?

1 Answer
Jun 16, 2017

#(r,theta)in{(3/2,pi/6+2kpi),(3/2,(5pi)/6+kpi)}, kinZZ#

Explanation:

If
#color(white)("XXX")r=4-5sin(theta)#
#color(white)("XXX")r=3sin(theta)#
then
#color(white)("XXX")3sin(theta)=4-5sin(theta)#

#color(white)("XXX")8sin(theta)=4#

#color(white)("XXX")sin(theta)=1/2#

For #theta in [0,2pi)#
#color(white)("XXX")theta=pi/6color(white)("xxxxxxx")orcolor(white)("xx")theta=(5pi)/6#
or to be complete
#color(white)("XXX")theta=pi/6+2kpicolor(white)("xx")orcolor(white)("xx")theta=(5pi)/6+2kpicolor(white)("XXX")kinZZ#

and since #r=3sin(theta)#
#color(white)("XXX")r=3*1/2 = 3/2#