I like students to understand what is happening.
A polar coordinate point of (2,2π/3) means
point an arm 2π/3 radians or 120 degrees.
make the arm 2 units in length
Now from the end of that arm, drop a perpendicular to form a right-angled triangle in the second quadrant.
You should recognize the 30-60-90 triangle whose sides are in the ratio of 1 : √3 : 2
Our hypotenuse of 2 matches this perfectly,
so x = -1, y = √3
and the rectangular coordinate point is (-1,√3)
of course you could just plug into formulas
x = rcosØ = 2cos 120 = 2(-1/2) = -1
y = rsinØ = 2(√3/2) = √3
convert polar to rectangular
2,2pi/3
?????
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