How do you express the Cartesian coordinates (3, - 4) as polar coordinates?

2 Answers
Leland Adriano Alejandro
May 15, 2016

Polar Coordinates #(5, 306.86989765^@)#
OR
Polar Coordinates #(5, -53.13010235^@)#

Explanation:

Given: #x=3# and #y=-4#

#r=sqrt(x^2+y^2)=sqrt(3^2+(-4)^2)=sqrt(25)=5#

#theta=tan^-1 (y/x)=tan^-1 (-4/3)=306.86989765^@#

God bless....I hope the explanation is useful.

Cesareo R.
May 15, 2016

#(r,theta) = 5 angle -0.927295[radian] #

Explanation:

The pass equations are
#x = r cos(theta)#
#y = r sin(theta)#
and dividing each equation side
#y/x=tan(theta)# and also its inverse function
#theta = arctan(y/x)#
also #x^2+y^2=r^2cos(theta)^2+r^2sin(theta)^2 = r^2(cos(theta)^2+sin(theta)^2)=r²#
Applying all those formulas we get
#3^2+(-4)^2=r^2=25 = 5^2#
#theta = arctan(-4/3) =-0.927295[radian] #

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