Calculus Examples

$(- 1, - \sqrt{3})$

Step 1

Use the conversion formulas to convert from polar coordinates to rectangular coordinates.

$x = r c o s θ$

$y = r s i n θ$

Step 2

Substitute in the known values of $r = - 1$ and $θ = - \sqrt{3}$ into the formulas.

$x = (- 1) \cos (- \sqrt{3})$

$y = (- 1) \sin (- \sqrt{3})$

Step 3

Evaluate $\cos (- \sqrt{3})$ .

$x = - 1 \cdot - 0.16055653$

$y = (- 1) \sin (- \sqrt{3})$

Step 4

Multiply $- 1$ by $- 0.16055653$ .

$x = 0.16055653$

$y = (- 1) \sin (- \sqrt{3})$

Step 5

Evaluate $\sin (- \sqrt{3})$ .

$x = 0.16055653$

$y = - 1 \cdot - 0.98702664$

Step 6

Multiply $- 1$ by $- 0.98702664$ .

$x = 0.16055653$

$y = 0.98702664$

Step 7

The rectangular representation of the polar point $(- 1, - \sqrt{3})$ is $(0.16055653, 0.98702664)$ .

$(0.16055653, 0.98702664)$