Precalculus Examples

$(\frac{4}{5}, \frac{- 3}{5})$

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 $r = \frac{4}{5}$ and $θ = \frac{- 3}{5}$ into the formulas.

$x = (\frac{4}{5}) \cos (\frac{- 3}{5})$

$y = (\frac{4}{5}) \sin (\frac{- 3}{5})$

Step 3

Move the negative in front of the fraction.

$x = \frac{4}{5} \cdot \cos (- \frac{3}{5})$

$y = (\frac{4}{5}) \sin (\frac{- 3}{5})$

Step 4

Evaluate $\cos (- \frac{3}{5})$ .

$x = \frac{4}{5} \cdot 0.82533561$

$y = (\frac{4}{5}) \sin (\frac{- 3}{5})$

Step 5

Multiply $\frac{4}{5} \cdot 0.82533561$ .

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Step 5.1

Combine $\frac{4}{5}$ and $0.82533561$ .

$x = \frac{4 \cdot 0.82533561}{5}$

$y = (\frac{4}{5}) \sin (\frac{- 3}{5})$

Step 5.2

Multiply $4$ by $0.82533561$ .

$x = \frac{3.30134245}{5}$

$y = (\frac{4}{5}) \sin (\frac{- 3}{5})$

$x = \frac{3.30134245}{5}$

$y = (\frac{4}{5}) \sin (\frac{- 3}{5})$

Step 6

Divide $3.30134245$ by $5$ .

$x = 0.66026849$

$y = (\frac{4}{5}) \sin (\frac{- 3}{5})$

Step 7

Move the negative in front of the fraction.

$x = 0.66026849$

$y = \frac{4}{5} \cdot \sin (- \frac{3}{5})$

Step 8

Evaluate $\sin (- \frac{3}{5})$ .

$x = 0.66026849$

$y = \frac{4}{5} \cdot - 0.56464247$

Step 9

Multiply $\frac{4}{5} \cdot - 0.56464247$ .

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Step 9.1

Combine $\frac{4}{5}$ and $- 0.56464247$ .

$x = 0.66026849$

$y = \frac{4 \cdot - 0.56464247}{5}$

Step 9.2

Multiply $4$ by $- 0.56464247$ .

$x = 0.66026849$

$y = \frac{- 2.25856989}{5}$

$x = 0.66026849$

$y = \frac{- 2.25856989}{5}$

Step 10

Divide $- 2.25856989$ by $5$ .

$x = 0.66026849$

$y = - 0.45171397$

Step 11

The rectangular representation of the polar point $(\frac{4}{5}, \frac{- 3}{5})$ is $(0.66026849, - 0.45171397)$ .

$(0.66026849, - 0.45171397)$