Trigonometry Examples

$(\sqrt{3}, \frac{π}{2})$

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 $r = \sqrt{3}$ and $θ = \frac{π}{2}$ into the formulas.

$x = (\sqrt{3}) \cos (\frac{π}{2})$

$y = (\sqrt{3}) \sin (\frac{π}{2})$

Step 3

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$x = \sqrt{3} \cdot 0$

$y = (\sqrt{3}) \sin (\frac{π}{2})$

Step 4

Multiply $\sqrt{3}$ by $0$ .

$x = 0$

$y = (\sqrt{3}) \sin (\frac{π}{2})$

Step 5

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

$x = 0$

$y = \sqrt{3} \cdot 1$

Step 6

Multiply $\sqrt{3}$ by $1$ .

$x = 0$

$y = \sqrt{3}$

Step 7

The rectangular representation of the polar point $(\sqrt{3}, \frac{π}{2})$ is $(0, \sqrt{3})$ .

$(0, \sqrt{3})$