1 the polar questions of a point are given find the rectangu

1. the polar questions of a point are given. find the rectangular coordinates of the point

(-5 , 3pi/4)

2. the rectangular coordinates of a point are given find polar coordinates for the point.

(-5,5)

Solution

Polar coordinate   (-5,3pi/4)

Here R= -5 and theta=3pi/4

x=R cos theta= -5 cos 3pi/4=3.54

y=R sin theta= -5 sin 3pi/4=-3.54

Required rectangular coordinate (3.54,-3.54)

2.    Given rectangular coordinate (-5,5)

R=sqrt(x²+ y²)= sqrt((-5)²+5²) = 5sqrt2

theta=tan^-1(y/x)= tan^-1(5/-5) = 3pi/4

Required polar coordinate=(5sqrt2, 3pi/4)