Question

Determine the following for a point with the rectangular coordinates (1.380, 2.690) m.

(a) the polar coordinates r and θ (Enter your answers to at least three significant figures.)

r	= m
θ	= °

(b) the rectangular coordinates of the point with the polar coordinates

(2r, θ)

x	= m
y	= m

(c) the rectangular coordinates of the point with the polar coordinates

(r, 2θ)

x	= m
y	= m

Answer 1

Conversion of Rectangular Coordinates into Polar coordinates is given by:

Suppose P (x1, y1), then,

r1 = sqrt (x1^2 + y1^2)

= arctan (y1/x1)

And if P (r1, ), then

x1 = r1*cos

y1 = r1*sin

Part A. given that P (1.380, 2.690) m

So,

r = sqrt (1.380^2 + 2.690^2)

r = 3.0233 m

= arctan (2.690/1.380)

= 62.84 deg

Part B. Now when Q (2r, )

Since r = 3.0233, So 2r = 6.0466 m & = 62.84 deg, So

Q (2r, ) = (6.0466, 62.84 deg)

x = 6.0466*cos 62.84 deg = 2.760 m

y = 6.0466*sin 62.84 deg = 5.380 m

Part B. Now when R (r, 2)

Since r = 3.0233, & = 62.84 deg, So 2 = 125.68 deg

R (r, 2) = (3.0233, 125.68 deg)

x = 3.0233*cos 125.68 deg = -1.763 m

y = 3.0233*sin 125.68 deg = 2.456 m

Let me know if you've any query.