TrueFalse on both partsSolutionWe know the relation between

True/False on both parts:

Solution

We know the relation between polar and cartesian coordinates

r = sqrt (x^2 +y^2)

and theta = tan^-1 (y/x)

hence r= sqrt (1^2 +0^2 ) = sqrt(1) = 1

and theta = tan^1 (0/1) = tan^-1 (0) = 0

hence in polar we have (r, thata) = (1,0)

Hence the statement is correct. True

b)

we have x= 1/sqrt2 , y= 1/sqrt2 in caretesian coordinates

hence r= sqrt( 1/2+ 1/2) = sqrt (1) = 1

and theta = tan^-1 (1/sqrt2 / 1/sqrt2) = tan^-1 (1) = pi/4

Hence in polar we have (r,thata) = (1, pi/4)

Hence the statement is correct. true