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Convert Cartesian coordinate into polar ...

Convert Cartesian coordinate into polar coordinate
`(-1, sqrt3)`

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Here the Cartesian coordinate of the point `(x,y)=(-1, sqrt3)`
`therefore x=-1, y=sqrt3`
`therefore r^2=x^2+y^2`
`implies r^2=(-1)^2+(sqrt3)^2=4`
`implies r=2`
Also, `tantheta=-sqrt3/1 = -"tan"pi/3=tan(pi-pi/3)`
Since the point is in the second quadrant
`therefore theta=(2pi)/3`
Here the polar coordinate of the point is `(2, (2pi)/3)`
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MAHAVEER PUBLICATION-CARTESIAN AND POLAR COORDINATE SYSTEM-QUESTION BANK
  1. Convert Cartesian coordinate into polar coordinate (2,2)

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  2. Convert Cartesian coordinate into polar coordinate (1, -sqrt3)

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  3. Convert Cartesian coordinate into polar coordinate (-1, sqrt3)

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  4. Find the distance between the points (5,3) and (-2,4)

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  5. Find a point on the xaxis, which is equidistant from the points (7,...

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  6. Find the distance between the points P(2,pi/2) and Q(3,pi/4) which are...

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  7. Convert the rectangular equation of a circle x^2+y^2=c^2 to a polar eq...

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  8. Prove that the diagonals of a rectangle are equal.

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  9. Show that the points P(-1, -1), Q(2,3) and R(2,6) are the vertices of ...

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  10. Show that the points A(1,2), B(4,5) and C(-1,0) lie on a straight line...

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  11. Find the distance between the following pair of points (5,4) and (2,-3...

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  12. Find the distance between the following pair of points (a,-a) and (b,b...

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  13. Plot the following polar coordinates: (3, (7pi)/4)

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  14. Plot the following polar coordinates: (-2, (5pi)/2)

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  15. Plot the following polar coordinates: (3,-pi/3)

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  16. Plot the following polar coordinates: (-3, -(3pi)/4)

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  17. Convert into polar coordinates: (-3,3)

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  18. Convert into polar coordinates: (0,6)

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  19. Convert into polar coordinates: (-1,sqrt3)

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  20. Convert into Cartesian coordinates: (6/sqrt2, pi/4)

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