Precalculus Examples

$(1, - \frac{π}{2})$

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 $r = 1$ and $θ = - \frac{π}{2}$ into the formulas.

$x = (1) \cos (- \frac{π}{2})$

$y = (1) \sin (- \frac{π}{2})$

Step 3

Multiply $\cos (- \frac{π}{2})$ by $1$ .

$x = \cos (- \frac{π}{2})$

$y = (1) \sin (- \frac{π}{2})$

Step 4

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

$x = \cos (\frac{3 π}{2})$

$y = (1) \sin (- \frac{π}{2})$

Step 5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$x = \cos (\frac{π}{2})$

$y = (1) \sin (- \frac{π}{2})$

Step 6

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

$x = 0$

$y = (1) \sin (- \frac{π}{2})$

Step 7

Multiply $\sin (- \frac{π}{2})$ by $1$ .

$x = 0$

$y = \sin (- \frac{π}{2})$

Step 8

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

$x = 0$

$y = \sin (\frac{3 π}{2})$

Step 9

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

$x = 0$

$y = - \sin (\frac{π}{2})$

Step 10

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

$x = 0$

$y = - 1 \cdot 1$

Step 11

Multiply $- 1$ by $1$ .

$x = 0$

$y = - 1$

Step 12

The rectangular representation of the polar point $(1, - \frac{π}{2})$ is $(0, - 1)$ .

$(0, - 1)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$