Question

The point $(r,\theta)$ in polar coordinates is $(7,5)$ in rectangular coordinates. what is the point $\left( 2r, \theta + \frac{\pi}{2} \right)$ in rectangular coordinates?

Answer 1

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

Answer:

x=r cos(theta) y=rcos(theta)

Step-by-step explanation:

Tan(theta)=cos/sin as well as x/y therefore cos=x and sin=y

Wrong question sry didnt read