The cartesian coordinates of a point are (1,1). (i) find polar coordinates (r,\theta) of the point, where r> 0 and 0 \le \theta < 2\pi.

R = √(x^2 +y^2) = √2

θ = arctan(y/x) = arctan(1) = π/4 . . . . . taking quadrant into account*

(1, 1) in rectangular coordinates = (√2, π/4) in polar coordinates.

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* if you do this using a spreadsheet or some calculators, the ATAN2(x, y) function is appropriate. Be careful, on my TI-83/84, it is ATAN2(y, x).