Question

The polar coordinates of a certain point are (r = 4.35 cm, θ = 190°).

(a) Find its Cartesian coordinates x and y.

x	=  cm
y	=  cm

(b) Find the polar coordinates of the points with Cartesian coordinates (−x, y).

r	=  cm
θ	=  °

(c) Find the polar coordinates of the points with Cartesian coordinates (−2x, −2y).

r	=  cm
θ	=  °

(d) Find the polar coordinates of the points with Cartesian coordinates (3x, −3y).

r	=  cm
θ	=  °

Answer 1

here,

r = 4.35 cm

theta = 190 degree

a)

x1 = r * cos(theta) = 4.35 * cos(190) = - 4.28 cm

y1 = r * sin(theta) = 4.35 * sin(190) = - 0.76 cm

b)

for (x2 , y2 ) = ( - x1 , y1) = ( 4.28 cm , - 0.76 cm)

r2 = sqrt(4.28^2 + 0.76^2) = 4.35 cm

theta2 = arctan((-0.76)/4.28) = 350 degree

c)

for (x3 , y3 ) = ( - 2 x2 , - 2 y2) = ( 8.56 cm , 1.52 cm)

r3 = sqrt(8.56^2 + 1.52^2) = 8.7 cm

theta2 = arctan((1.52)/8.56) = 10 degree

d)

for (x3 , y3 ) = ( 3 x1 ,- 3 y1) = ( - 12.84 cm , 2.28 cm)

r3 = sqrt(12.84^2 + 2.28^2) = 13.05 cm

theta3 = arctan(2.28 /(12.84)) = 170 degree