What are the components of the vector between the origin and the polar coordinate #(-16, (-pi)/4)#?

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Answer 1 · 2018-02-27T05:06:53

#x = -16 * cos (-pi/4 )= -16 * (1/sqrt2) = color (green)(-8sqrt2#

#y = -16 * sin (-pi/4 )= -16 * (-1/sqrt2) = color (green)(8sqrt2#

We can use the following formulas to convert polar to Cartesian coordinates.

#x = r cos theta, y = r sin theta #

#Given : [r,theta] = [-16, -pi/4]#

#x = -16 * cos (-pi/4 )= -16 * (1/sqrt2) = color (green)(-8sqrt2#

#y = -16 * sin (-pi/4 )= -16 * (-1/sqrt2) = color (green)(8sqrt2#

#tan theta = tan (-pi/4) = -1#