Precalculus Examples

$(5, \frac{π}{6})$

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 $r = 5$ and $θ = \frac{π}{6}$ into the formulas.

$x = (5) \cos (\frac{π}{6})$

$y = (5) \sin (\frac{π}{6})$

Step 3

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$x = 5 (\frac{\sqrt{3}}{2})$

$y = (5) \sin (\frac{π}{6})$

Step 4

Combine $5$ and $\frac{\sqrt{3}}{2}$ .

$x = \frac{5 \sqrt{3}}{2}$

$y = (5) \sin (\frac{π}{6})$

Step 5

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$x = \frac{5 \sqrt{3}}{2}$

$y = 5 (\frac{1}{2})$

Step 6

Combine $5$ and $\frac{1}{2}$ .

$x = \frac{5 \sqrt{3}}{2}$

$y = \frac{5}{2}$

Step 7

The rectangular representation of the polar point $(5, \frac{π}{6})$ is $(\frac{5 \sqrt{3}}{2}, \frac{5}{2})$ .

$(\frac{5 \sqrt{3}}{2}, \frac{5}{2})$