Convert to Rectangular Coordinates (4,pi/4)

$(4, \frac{π}{4})$

Use the conversion formulas to convert from polar coordinates to rectangular coordinates.

$x = r c o s θ$

$y = r s i n θ$

Substitute in the known values of $r = 4$ and $θ = \frac{π}{4}$ into the formulas.

$(4) \cos (\frac{π}{4})$

$y = (4) \sin (\frac{π}{4})$

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

$x = 4 (\frac{\sqrt{2}}{2})$

$y = (4) \sin (\frac{π}{4})$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

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

$y = (4) \sin (\frac{π}{4})$

Cancel the common factor.

$x = 2 \cdot (2 (\frac{\sqrt{2}}{2}))$

$y = (4) \sin (\frac{π}{4})$

Rewrite the expression.

$x = 2 \sqrt{2}$

$y = (4) \sin (\frac{π}{4})$

$x = 2 \sqrt{2}$

$y = (4) \sin (\frac{π}{4})$

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

$x = 2 \sqrt{2}$

$y = 4 (\frac{\sqrt{2}}{2})$

Cancel the common factor of $2$ .

Tap for more steps…

Factor $2$ out of $4$ .

$x = 2 \sqrt{2}$

$y = 2 (2) (\frac{\sqrt{2}}{2})$

Cancel the common factor.

$x = 2 \sqrt{2}$

$y = 2 \cdot (2 (\frac{\sqrt{2}}{2}))$

Rewrite the expression.

$x = 2 \sqrt{2}$

$y = 2 \sqrt{2}$

$x = 2 \sqrt{2}$

$y = 2 \sqrt{2}$

The rectangular representation of the polar point $(4, \frac{π}{4})$ is $(2 \sqrt{2}, 2 \sqrt{2})$ .

$(2 \sqrt{2}, 2 \sqrt{2})$

Convert to Rectangular Coordinates (4,pi/4)

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