The rectangular coordinates of a point are given Find polar

The rectangular coordinates of a point are given. Find polar coordinates of the point such that r > 0 and 0 lessthanorequalto 2pi. (1.-1) The polar coordinates are (Type an ordered pair. Type your answer in radians. Type an exact answer. Simplify your answer.)

Solution

given rectangular points are (1,-1)

so (x,y) = (rcos,rsin) --> in polar

(1,-1) = (rcos,rsin)

rcos = 1 and rsin =-1

r^2cos^2 = 1^2 and r^2sin^2 =1

add these two

r^2cos^2 + r^2sin^2 = 1+1

r^2(cos^2 + sin^2) =2

r^2 (1) =2

r = sqrt(2)

now divide rsin/rcos = -1/1

tan =-1

tan , sin are negative and cos is positive , so is in 4th quadrant (QIV)

so is in 2 - /4 = 7/4

so polar coordinates are (r, ) =(sqrt2 , 7/4)