How do you find the polar coordinates given the rectangular coordinates (3,8)?

1 Answer
Douglas K.
Nov 18, 2016

Please see the explanation.

Explanation:

The polar coordinate system is an ordered pair #(r,theta)#

To convert from Cartesian, #(x, y)# to r:

#r = sqrt(x^2 + y^2)#

To convert from Cartesian, #(x, y)# to #theta#:

If #x > 0 and y >= 0#, then use: #theta = tan^-1(y/x)" [1]"#
If #x = 0 and y > 0#, then use: #theta = pi/2" [2]"#
If #x = 0 and y < 0#, then use: #theta = (3pi)/3" [3]"#
If #x < 0#, then use: #theta = pi + tan^-1(y/x)" [4]"#
If #x > 0 and y < 0#, then use: #theta = 2pi + tan^-1(y/x)" [5]"#

For your point, #(3, 8)#:

#r = sqrt(3^2 + 8^2) = sqrt(73) " length units"#

Use equation [1]:

#theta = tan^-1(8/3)#

#theta ~~ 1.249 " radians"#

The polar point is #(sqrt(73)" length units", 1.249" radians")#

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