The rectangular coordinates will be (x=7cot(θ), y=7).
A pair of coordinates locating the position of a point in a plane, the first being the length of the straight line ( r ) connecting the point to the origin, and the second the angle ( θ ) made by this line with a fixed line.
We have the standard conversion toolbox:
[tex]x=rcos(\theta)\\\\y=rsin(\theta)[/tex]
Here it is given that
[tex]r=7cosec(\theta)[/tex]
so
[tex]x=7cosec(\theta)\times cos(\theta)=\dfrac{7cos(\theta)}{sin(\theta )}=7cot(\theta)\\\\\\y=7cosec(\theta)\times sin(\theta)=\dfrac{7sin(\theta)}{sin(\theta)} = 7[/tex]
therefore the rectangular coordinates are (7cot(θ), 7)
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