Express( 4,-4)in polar coordinates?

Question

1138 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-05T02:01:26

#(4sqrt2, (7pi)/4)# (radians) or #(4sqrt2, 315^@)# (degrees)

Rectangular #-># Polar: #(x, y) -> (r, theta)#

Find #r# (radius) using #r = sqrt(x^2 + y^2)#
Find #theta# by finding the reference angle: #tantheta = y/x# and use this to find the angle in the correct quadrant

#r = sqrt((4)^2 + (-4)^2)#

#r = sqrt(16 + 16)#

#r = sqrt32#

#r = sqrt(16 * 2)#

#r = 4sqrt2#

Now we find the value of #theta# using #tantheta = y/x#.

#tantheta = -4/4#

#tantheta = -1#

#theta = tan^-1(-1)#

#theta = (3pi)/4# or #(7pi)/4#

To determine which one it is, we have to look at our coordinate #(4, -4)#. First, let's graph it:
enter image source here

As you can see, it is in the fourth quadrant. Our #theta# has to match that quadrant, meaning that #theta = (7pi)/4#.

From #r# and #theta#, we can write our polar coordinate:
#(4sqrt2, (7pi)/4)# (radians) or #(4sqrt2, 315^@)# (degrees)

Hope this helps!