Coordinate Geometry-15

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Write the polar coordinates of the point (4, 4)

Solution: x = r cos Θ = 4; ......................................(1)

y = r sin Θ = 4 .......................................................(ii)

Squaring and adding (i) and (ii)

r² (cos² Θ + sin² Θ) = 4² + 4² = 32

i.e. r² = 32 Therefore, r = √32 = √(16 x 2) = 4 √2

Dividing (ii) by (i)

tan Θ = 4/4 = 1. Therefore, Θ = 45⁰

Hence, the polar coordinates of the point are (4√2, 45⁰)