The rectangular coordinates of a point are given. Find the polar coordinates of each point in (r,theta) form.

Question

The rectangular coordinates of a point are given. Find the polar coordinates of each point in form.

A.

Use the appropriate conversion rules to write the coordinates of this point in polar form.

B. (0,7)

Use the appropriate conversion rules to write the coordinates of this point in polar form.

Answer 1

(-4, 4sqr3) =

x = rcosT, y = rsinT

r^2 = x^2 + y^2

y = 4sinT=8sqr3/2, r = 8, sinT = sqr3/2, T = arcsin(sqr3/2) = 60 degrees = pi/3 radians

x =( -8, pi/3)= (8, 240 degrees)= endless other polar forms, that is zero degrees or 0 radians

next

(0,7) = (7, 0) in polar form, surprise coincidence

helps just to plot and graph the point

Answer 2

(0,7)

Since y>0 and x=0, the angle i pi./2

The distance r is 7.

(7,pi/2)

Answer 3

r = distance from (0,0) to (-4, 4√3) = √[16 + 48] = 8

θ = positive angle with vertex (0,0), initial side the positive x-axis, and terminal side passing through the point (-4, 4√3). So, θ = π - Tan^-1(4√3 / 4) = π - π/3 = 2π/3.

Therefore, (r, θ) = (8, 2π/3)

x = rcosθ and y = rsinθ

(x, y) = (-4, 4√3) = (8cos(2π/3), 8sin(2π/3))

Part B can be done in a similar manner.