Answer: Given:
(r, θ) is equivalent to (x, y) = (7, 5).
By definition,
r = √(7² + 5²) = 8.6023
θ = tan⁻¹ (7/5) = 0.9505 rad
Therefore
2r = 17.2047
θ + π/2 = 0.9505 + π/2 = 2.5213
In rectangular coordinates,
x = 2r cos(θ + π/2) = 17.2047*cos(2.5213) = -14
y = 2r sin(θ + π/2) = 17.2047*sin(2.5213) = 10
Answer: (-14, 10)
