Precalculus Examples

$(π, π)$

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 $r = π$ and $θ = π$ into the formulas.

$x = (π) \cos (π)$

$y = (π) \sin (π)$

Step 3

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

$x = π (- \cos (0))$

$y = (π) \sin (π)$

Step 4

The exact value of $\cos (0)$ is $1$ .

$x = π (- 1 \cdot 1)$

$y = (π) \sin (π)$

Step 5

Multiply $- 1$ by $1$ .

$x = π \cdot - 1$

$y = (π) \sin (π)$

Step 6

Move $- 1$ to the left of $π$ .

$x = - 1 \cdot π$

$y = (π) \sin (π)$

Step 7

Rewrite $- 1 π$ as $- π$ .

$x = - π$

$y = (π) \sin (π)$

Step 8

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

$x = - π$

$y = π \sin (0)$

Step 9

The exact value of $\sin (0)$ is $0$ .

$x = - π$

$y = π \cdot 0$

Step 10

Multiply $π$ by $0$ .

$x = - π$

$y = 0$

Step 11

The rectangular representation of the polar point $(π, π)$ is $(- π, 0)$ .

$(- π, 0)$