Trigonometry Examples

$(- 5, \frac{5 π}{2})$

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 $r = - 5$ and $θ = \frac{5 π}{2}$ into the formulas.

$x = (- 5) \cos (\frac{5 π}{2})$

$y = (- 5) \sin (\frac{5 π}{2})$

Step 3

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$x = - 5 \cos (\frac{π}{2})$

$y = (- 5) \sin (\frac{5 π}{2})$

Step 4

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

$x = - 5 \cdot 0$

$y = (- 5) \sin (\frac{5 π}{2})$

Step 5

Multiply $- 5$ by $0$ .

$x = 0$

$y = (- 5) \sin (\frac{5 π}{2})$

Step 6

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$x = 0$

$y = - 5 \sin (\frac{π}{2})$

Step 7

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

$x = 0$

$y = - 5 \cdot 1$

Step 8

Multiply $- 5$ by $1$ .

$x = 0$

$y = - 5$

Step 9

The rectangular representation of the polar point $(- 5, \frac{5 π}{2})$ is $(0, - 5)$ .

$(0, - 5)$