How do you convert # (-6,-3)# into polar coordinates?

1 Answer
Feb 13, 2016

Answer:

Polar coordinates of #(−6,−3)# are #(3sqrt5, 206.565^o)#

Explanation:

If #(x, y)# are converted into polar coordinates #(r, theta)#,

while #(x, y)# in terms of #r# and #theta# are #x=rcostheta# and #y=rsintheta#, #(r, theta)# in terms of #x# and #y# are #r=sqrt(x^2+y^2)# and #theta=tan^-1(y/x)#

Hence, converting #(−6,−3)# into polar coordinates

#r=sqrt((-6)^2+(-3^2)# = #sqrt45# = #3sqrt5#

#theta=tan^-1((-3)/-6)# = #tan^-1(1/2)#. Further, as #(−6,−3)# is in third quadrant #theta=(180+26.565)=206.565^o#

Hence polar coordinates of #(−6,−3)# are #(3sqrt5, 206.565^o)#