Convert (4, 5π/6) to rectangular form?

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Answer 1 · 2018-05-23T07:46:40

rectangular form:

#(x,y)=(-2sqrt3,2)#

show:

#x=r*costheta#

#y=r*sintheta#

#x=4*cos(5pi/6)=4*(-sqrt3/2)=-2sqrt3#

#y=4*sin(5pi/6)=4*1/2=2#

rectangular form:

#(x,y)=(-2,2)#

Note that:

#5pi/6=150# lies in the second quadrant

since #costheta# is negative in the second quadrant

#cos(5pi/6)=-cos(pi/6)=-sqrt3/2#

since #sintheta# is positive in the second quadrant

#sin(5pi/6)=sin(pi/6)=1/2#