Precalculus Examples

$(- 5.5, \frac{π}{4})$

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 $r = - 5.5$ and $θ = \frac{π}{4}$ into the formulas.

$x = (- 5.5) \cos (\frac{π}{4})$

$y = (- 5.5) \sin (\frac{π}{4})$

Step 3

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$x = - 5.5 \frac{\sqrt{2}}{2}$

$y = (- 5.5) \sin (\frac{π}{4})$

Step 4

Multiply $- 5.5 \frac{\sqrt{2}}{2}$ .

Tap for more steps...

Step 4.1

Combine $- 5.5$ and $\frac{\sqrt{2}}{2}$ .

$x = \frac{- 5.5 \sqrt{2}}{2}$

$y = (- 5.5) \sin (\frac{π}{4})$

Step 4.2

Multiply $- 5.5$ by $\sqrt{2}$ .

$x = \frac{- 7.77817459}{2}$

$y = (- 5.5) \sin (\frac{π}{4})$

$x = \frac{- 7.77817459}{2}$

$y = (- 5.5) \sin (\frac{π}{4})$

Step 5

Divide $- 7.77817459$ by $2$ .

$x = - 3.88908729$

$y = (- 5.5) \sin (\frac{π}{4})$

Step 6

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$x = - 3.88908729$

$y = - 5.5 \frac{\sqrt{2}}{2}$

Step 7

Multiply $- 5.5 \frac{\sqrt{2}}{2}$ .

Tap for more steps...

Step 7.1

Combine $- 5.5$ and $\frac{\sqrt{2}}{2}$ .

$x = - 3.88908729$

$y = \frac{- 5.5 \sqrt{2}}{2}$

Step 7.2

Multiply $- 5.5$ by $\sqrt{2}$ .

$x = - 3.88908729$

$y = \frac{- 7.77817459}{2}$

$x = - 3.88908729$

$y = \frac{- 7.77817459}{2}$

Step 8

Divide $- 7.77817459$ by $2$ .

$x = - 3.88908729$

$y = - 3.88908729$

Step 9

The rectangular representation of the polar point $(- 5.5, \frac{π}{4})$ is $(- 3.88908729, - 3.88908729)$ .

$(- 3.88908729, - 3.88908729)$