Question

convert the polar coordinates (5, 6.1) to rectangular coordinates.
(0.98, -0.18)
(0.98, 0.18)
(4.92, -0.91)
(4.92, 0.91)

Explanation:

Step1: Recall conversion formulas

For polar coordinates $(r,\theta)$ to rectangular coordinates $(x,y)$, $x = r\cos\theta$ and $y=r\sin\theta$. Here $r = 5$ and $\theta=6.1$.

Step2: Calculate x - coordinate

$x = 5\cos(6.1)$. Using a calculator, $\cos(6.1)\approx0.984$, so $x = 5\times0.984 = 4.92$.

Step3: Calculate y - coordinate

$y = 5\sin(6.1)$. Using a calculator, $\sin(6.1)\approx - 0.178$, so $y=5\times(-0.178)=-0.89\approx - 0.91$.

Answer:

C. (4.92, -0.91)