Precalculus Examples

$(- 2, - 360)$

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 $r = - 2$ and $θ = - 360$ into the formulas.

$x = (- 2) \cos (- 360)$

$y = (- 2) \sin (- 360)$

Step 3

Add full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$x = - 2 \cos (0)$

$y = (- 2) \sin (- 360)$

Step 4

The exact value of $\cos (0)$ is $1$ .

$x = - 2 \cdot 1$

$y = (- 2) \sin (- 360)$

Step 5

Multiply $- 2$ by $1$ .

$x = - 2$

$y = (- 2) \sin (- 360)$

Step 6

Add full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$x = - 2$

$y = - 2 \sin (0)$

Step 7

The exact value of $\sin (0)$ is $0$ .

$x = - 2$

$y = - 2 \cdot 0$

Step 8

Multiply $- 2$ by $0$ .

$x = - 2$

$y = 0$

Step 9

The rectangular representation of the polar point $(- 2, - 360)$ is $(- 2, 0)$ .

$(- 2, 0)$