Question

What are the rectangular coordinates of the polar coordinates %7B%5Cpi%20%7D%7B12%7D%20%29" id="TexFormula1" title="(2\sqrt{2} ,-\frac{\pi }{12} )" alt="(2\sqrt{2} ,-\frac{\pi }{12} )" align="absmiddle" class="latex-formula">
Enter your answer in the box. Enter values rounded to the nearest hundredth.

Answer 1

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)

Answer 2

Do you still need help ?!?!