Precalculus Examples

$(23, 65)$

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 $r = 23$ and $θ = 65$ into the formulas.

$x = (23) \cos (65)$

$y = (23) \sin (65)$

Step 3

Evaluate $\cos (65)$ .

$x = 23 \cdot 0.42261826$

$y = (23) \sin (65)$

Step 4

Multiply $23$ by $0.42261826$ .

$x = 9.72022002$

$y = (23) \sin (65)$

Step 5

Evaluate $\sin (65)$ .

$x = 9.72022002$

$y = 23 \cdot 0.90630778$

Step 6

Multiply $23$ by $0.90630778$ .

$x = 9.72022002$

$y = 20.8450791$

Step 7

The rectangular representation of the polar point $(23, 65)$ is $(9.72022002, 20.8450791)$ .

$(9.72022002, 20.8450791)$