Precalculus Examples

$(8, 10)$

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 $r = 8$ and $θ = 10$ into the formulas.

$x = (8) \cos (10)$

$y = (8) \sin (10)$

Step 3

Evaluate $\cos (10)$ .

$x = 8 \cdot 0.98480775$

$y = (8) \sin (10)$

Step 4

Multiply $8$ by $0.98480775$ .

$x = 7.87846202$

$y = (8) \sin (10)$

Step 5

Evaluate $\sin (10)$ .

$x = 7.87846202$

$y = 8 \cdot 0.17364817$

Step 6

Multiply $8$ by $0.17364817$ .

$x = 7.87846202$

$y = 1.38918542$

Step 7

The rectangular representation of the polar point $(8, 10)$ is $(7.87846202, 1.38918542)$ .

$(7.87846202, 1.38918542)$

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