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" "Q2" => "Find the of the polar coordinates point whose Cartesian coordinates are.
(ii) \\(\\left(0, \\frac{1}{2}\\right)\\)

", "A2" => "Solution:
Here x = 0 and y = \\(\\frac{1}{2}\\)
the point lies on the positive side of Y-axis. Let the polar coordinates be (r, θ)
Then, r² = x² + y² = (0)² + \\(\\left(\\frac{1}{2}\\right)^{2}=0+\\frac{1}{4}=\\frac{1}{4}\\)
∴ r = \\(\\frac{1}{2}\\) …[∵ r > 0]
cosθ = \\(\\frac{x}{r}=\\frac{0}{(1 / 2)}\) = 0
and sin θ = \\(\\frac{y}{r}=\\frac{(1 / 2)}{(1 / 2)}\\) = 1
Since, the point lies on the positive side of Y-axis and 0 ≤ θ ≤ 2π
cosθ = 0 = cos\\(\\frac{\\pi}{2}\\) and sinθ = 1 = sin\\(\\frac{\\pi}{2}\\)
∴ θ = \\(\\frac{\\pi}{2}\\)
∴ the polar coordinates of the given point are \\(\\left(\\frac{1}{2}, \\frac{\\pi}{2}\\right)\\).", "Q3" => "Find the of the polar coordinates point whose Cartesian coordinates are.
(iii) \\((1,-\\sqrt{3})\\)

", "A3" => "Solution:
Here x = 1 and y = \\(-\\sqrt{3}\\)
∴ the point lies in the fourth quadrant.
Let the polar coordinates be (r, θ).
Then, r² = x² + y² = (1)² + (\\(-\\sqrt {3}\\) )² = 1 + 3 = 4
∴ r = 2 … [∵ r > 0]
" ); ?>

• Find the of the polar coordinates point whose Cartesian coordinates are.
  (i) \\((\\sqrt{2}, \\sqrt{2})\\)
  
  

  
  

  Solution:
  Here x = \\(\\sqrt {2}\\) and y = \\(\\sqrt {2}\\)
  ∴ the point lies in the first quadrant.
  Let the polar coordinates be (r, θ)
  Then, r² = x² + y² = (\\(\\sqrt {2}\\) )² + (\\(\\sqrt {2}\\) )

  ² = 2 + 2 = 4
  ∴ r = 2 … [∵ r > 0]
  cos θ = \\(\\frac{x}{r}=\\frac{\\sqrt{2}}{2}=\\frac{1}{\\sqrt{2}}\\)
  and sin θ = \\(\\frac{y}{r}=\\frac{\\sqrt{2}}{2}=\\frac{1}{\\sqrt{2}}\\)
  ∴ tan θ = 1
  Since the point lies in the first quadrant and
  0 ≤ θ ≤ 2π, tan θ = 1 = tan\\(\\frac{\\pi}{4}\\)
  ∴ θ = \\(\\frac{\\pi}{4}\\)
  ∴ the polar coordinates of the given point are \\(\\left(2, \\frac{\\pi}{4}\\right)\\).",