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In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.

-2,0

Short Answer

Expert verified

The polar coordinates are 2,2and-2,2k+1π, for any integer k.

Step by step solution

01

Step 1. Given information.

The given rectangular coordinate is:

-2,0

Herex=-2andy=0.

02

Step 2. Find the value of r.

To find the value of r, use the formula r=x2+y2:

r=-22+02r=4r=±2

03

Step 3. Find the value of θ.

Use the formula tanθ=yx,

tanθ=yx;thenθ=tan-1yxθ=tan-10-2θ=tan-10θ=π,2π

04

Step 4. Find the polar coordinates.

Take r=2,θ=2π;thenr,θ=2,2π,

The coordinates of r,θare2,2, for any integer k.


Now take r=-2,θ=π;thenr,θ=-2,π,

The coordinates of r,θare-2,2k+1π, for any integer k.


Therefore, all the polar coordinates are 2,2and-2,2k+1π, for any integer k.

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