How do you convert $r = 2 csc(theta)$ to rectangular form?

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Answer 1 · 2018-07-11T08:45:25

y = 2

$r >=2, csc theta >=1$

Conversion formula: $r ( cos theta, sin theta ) = ( x, y ),$

with $r = sqrt ( x^2 + y^2 ) >= 0$

For $theta ne kpi, k = 0, +-1, +-2, +-3, ...,$

Here, $r sin theta = y = 2$ . See graph for this straight line y = 2,

parallel to x-axis, at a height 2 units.

graph{y - 2 - 0.000000001 x = 0}

Please note that $theta in ( 0, pi)$ .

Some nuances, relating to this polar form:

Of course, the same line would be periodically created, for

$Q_1 and Q_2$ $theta in ( 2 k pi, (2 k + 1 ) pi ), k = 0, +-1, +-1, +-3, ...$

$r < 0$ , for $Q_3 and Q_4$

$theta in ( (2 k - 1 ) pi, 2 k pi ), k = 0, +-1, +-1, +-3, ...$

How do you convert r = 2 csc(theta) r = 2 csc(theta) to rectangular form?