How do you find the rectangular coordinates of the point with polar coordinates (−1, π3)?

Question

How do you find the rectangular coordinates of the point with polar coordinates (−1, π3)?

traciaul6y · Accepted Answer

Step 1
When trying to convert polar coords to rectangular coords or vice versa you need to be aware of a few equations.

\cos (θ) = \frac{x}{r} \to x = r \cos (θ)

\sin (θ) = \frac{y}{r} \to y = r \sin (θ)

\tan (θ) = \frac{y}{x} \to θ = \tan^{- 1} (\frac{y}{x})

x^{2} + y^{2} = r^{2} \to r = \sqrt{x^{2} + y^{2}}

Polar Coordinates

(r, θ) \to (- 1, \frac{π}{3})

Calculate the x-value

x = r \cos (θ)

x = (- 1) \times \cos (\frac{π}{3})

x = (- 1) (\frac{1}{2})

x = - \frac{1}{2}

Calculate the y-value

y = r \sin (θ)

y = (- 1) (\frac{\sqrt{3}}{2})

y = - \frac{\sqrt{3}}{2}

Rectangular Coordinates

(x, y) \to (- \frac{1}{2}, - \frac{\sqrt{3}}{2})

How do you find the rectangular coordinates of the point