Precalculus Examples

$(12, 34)$

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 $r = 12$ and $θ = 34$ into the formulas.

$x = (12) \cos (34)$

$y = (12) \sin (34)$

Step 3

Evaluate $\cos (34)$ .

$x = 12 \cdot 0.82903757$

$y = (12) \sin (34)$

Step 4

Multiply $12$ by $0.82903757$ .

$x = 9.94845087$

$y = (12) \sin (34)$

Step 5

Evaluate $\sin (34)$ .

$x = 9.94845087$

$y = 12 \cdot 0.5591929$

Step 6

Multiply $12$ by $0.5591929$ .

$x = 9.94845087$

$y = 6.71031484$

Step 7

The rectangular representation of the polar point $(12, 34)$ is $(9.94845087, 6.71031484)$ .

$(9.94845087, 6.71031484)$