Question

Convert the point P=(r,theta)to a rectangular coordinate of the form (x,y): (2,-pi/6)

Answer 1

Answer:

B. (x, y) = (√3, -1)

Explanation:

To convert from the polar form, (r, θ) to the rectangular form, use the formula below:

$(x,y)=(r\cos\theta,r\sin\theta)$

Thus, given the polar form:

$(2,-\frac{\pi}{6})$

Its rectangular form is:

$\begin{gathered} (x,y)=\left(2\cos\left(-\frac{\pi}{6}\right),2\sin\left(-\frac{\pi}{6}\right)\right) \\ =\left(2\times\frac{\sqrt{3}}{2},2\left(-\frac{1}{2}\right)\right) \\ =(\sqrt{3},-1) \end{gathered}$

The rectangular form, (x, y) = (√3, -1).

The correct option is B.