Given any Cartesian coordinates xy there are polar coordinat

Given any Cartesian coordinates, (x,y), there are polar coordinates (r,) with 2<2. (a) If (x,y)=(14,7) then (r,)=( , ), (b) If (x,y)=(17,10) then (r,)=( , ), (c) If (x,y)=(2,8) then (r,)=( , ), (d) If (x,y)=(9,8) then (r,)=( , ), (e) If (x,y)=(5,4) then (r,)=( , ), (f) If (x,y)=(0,9) then (r,)=(

Solution

a)

given (x,y)=(14,7)

r = sqrt(x² + y2) = sqrt(196 + 49) = sqrt245 = 7sqrt5

= tan^-1(y/x) = tan^-1(-1/2) = 26.565

(r,) = (7sqrt5 , 26.565)

(b)

(x,y)=(17,10)

r = sqrt(289+100) = sqrt(389)

    = tan^-1(-10/17) = -30.4655

(r,)=(sqrt389 , -30.4655)

(c)

(x,y)=(2,8)

r = sqrt(4+64) = sqrt(68) = 2sqrt17

   = tan^-1(8/2) = 75.9637

(r,)=(2sqrt17 , 755.9637)

(d)

(x,y)=(9,8)

r = sqrt(81+64) = sqrt145

= tan^-1(-8/9) =-41.6335

(r,)=(sqrt145 , -41.6335)

(e)

(x,y)=(5,4)

r = sqrt(25+16) = sqrt41

   = tan^-1(4/5) = 38.6598

(r,)=( sqrt41, 38.6598 )

(f)

(x,y)=(0,9)

r = sqrt(81) = 9

= tan^-1(0) = 90

(r,)=( 9, 90)