Polar to rectangular, not given r, but only θ?

Question

Write the equation using rectangular coordinates and simplify:

θ = 3

r isn't given, so how do you convert it?

Answer 1

First think about it logically, what is y = 3. Well, its a horizontal line that passes through y = 3. The way you can plot this on a graph is by plotting a few points

When x = 0, y = 3
When x = 5, y = 3
When x = 8, y = 3

Now lets look at θ = 3

When r = 1, θ = 3
When r = 5, θ = 3
When r = 8, θ = 3


There fore it is a line through the origin at an angle of 3.

To convert any equation from polar coordinates to rectangular coorodinates all you have to do is use the formulas:

r = sqrt(x^2 + y^2)
θ = arctan(y/x)

in this example you only need the second formula. Substitue for theta and solve for y.

Answer 2

Polar coordinates are of the form (r,attitude). The x coordinate is rcos(attitude) and the y coordinate is rsin(attitude). So rectangular coordinates could be: (7cos9pi/4,7sin9pi/4)=(7sqrt(2)/2, 7sqrt(2)/2) or C

Answer 3

y/x = tan(3)
y = xtan(3)
If 3 is in degrees
y = 0.0524x
If 3 is in radians
y = - 0.143x