How do you convert #(-4,pi/6)# to rectangular form?

1 Answer
AJ Speller
Oct 6, 2016

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

Explanation:

#(r,theta) => (-4,pi/6)#

#pi/6=30# degrees

This means we are working with the special triangle 30-60-90

30 degrees corresponds to #1# => OPPOSITE SIDE
60 degrees corresponds to #sqrt3# => ADJACENT SIDE
90 degrees corresponds to #2# => HYPOTENUS

cosine #=> (a d j) / (h y p)#
sine #=> (o p p) / (h y p)#

Make the necessary substitutions

#x=rcos(theta)=-4cos(pi/6)=-4(sqrt3/2)=-2sqrt3#
#y=rsin(theta)=-4sin(pi/6)=-4(1/2)=-2#

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

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