Convert the Cartesian coordinate (-1,-3) to polar coordinates, 0 ≤ θ < 2 π , r >0

Answer 1

) ( -1,-3) lies in Quadrant III. We obtain the r-component of the polar form using

r = √(x² † y²_{) =} √((-1)² † (-3)² ) _{=√ 10}

Using the tan-1 ( calculator) function you will obtain a value for θ in degrees in range (-π /2, π/2) .

However, to obtain θ over the range (0, 2π) it must be adjusted ( in addition to converted to radians).

The rule is

For θ in the range [π/2,π) add π to the calculator value

For θ in the range [π, 3π/2) add π to the calculator value

For θ in the range [3π/2, 2π) add 2π to the calculator value

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θ = tan-1 (-3/-1) = 1.249 radians = 71.56 degrees

You will need to adjust the value of θ in Quadrant III (as shown below) to get in in range

so θ = 1.249 radians + π radians ~ 1.249 radians +3.14 radians = 4.43 radians ~ 253.8 degrees

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so your final answer is r = √ 10 and θ = 4.43 radians which describes a point in polar coordinates in Quadrant III.

Answer 2

Start with conversion equations:

r ^ 2 = sqrt[ x ^ 2 + y ^ 2]

tan(Θ) = (y / x)

List the numbers you have:

x = -1

y = -3

Plug them in and solve!

Hope this helps!