SOLUTION: Please give the corresponding equations in rectangular coordinates? 1) r = π 2) θ = 6 3) r = 4/(3cosθ -sinθ ) 4) r^2 = 36/(9-13sin^2(θ) )

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Question 1044706: Please give the corresponding equations in rectangular coordinates?
1) r = π
2) θ = 6
3) r = 4/(3cosθ -sinθ )
4) r^2 = 36/(9-13sin^2(θ) )
Found 2 solutions by ikleyn, advanced_Learner:
Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.
Please give the corresponding equations in rectangular coordinates? 
1) r = .      <---   = ,  or   = .  It is the circle of the radius  centered at (0,0).

2)  = 6.      <---  = tan(6),  where tan(6) is the tangent of 6 radians (which is slightly less than 360 degs =  = 6.28 . . . )
                           In addition, y < 0, x > 0, since the angle  is in QIV (fourth quadrant).

                           So, it is the ray in the QIV.

3) r = 4/(3cosθ -sinθ )

4) r^2 = 36/(9-13sin^2(θ) )


Comment from student: Your answer in #2 is only partly correct. My calculus book says it is only y = (tan6)x.


My response: Thank you for your feedback.
My answer is fully correct.
Your calculus book is only partly correct.
The set of points = 6 is the ray starting at the origin of the coordinate system.
It is not a straight line.


Answer by advanced_Learner(501)   (Show Source): You can put this solution on YOUR website!
.
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