Find the polar co-ordinates of point whose Cartesian co-ordinates are (1,√3).
Question
Find the polar co-ordinates of point whose Cartesian co-ordinates are (1,√3).
Solution
To convert Cartesian coordinates to polar coordinates, we use the following formulas:
r = √(x² + y²) θ = atan(y/x)
Given the Cartesian coordinates (1, √3), we can substitute x = 1 and y = √3 into the formulas.
Step 1: Calculate r r = √((1)² + (√3)²) r = √(1 + 3) r = √4 r = 2
Step 2: Calculate θ θ = atan(√3 / 1) θ = atan(√3) θ = 60° (or π/3 in radians)
So, the polar coordinates of the point (1, √3) are (2, 60°) or (2, π/3) in radians.
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