Precalculus Examples

(2, - 6)

$(2, - 6)$

Step 1

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

x = r c o s θ

$x = r c o s θ$

y = r s i n θ

$y = r s i n θ$

Step 2

Substitute in the known values of

r = 2

$r = 2$ and

θ = - 6

$θ = - 6$ into the formulas.

x = (2) \cos (- 6)

$x = (2) \cos (- 6)$

y = (2) \sin (- 6)

$y = (2) \sin (- 6)$

Step 3

Evaluate

\cos (- 6)

$\cos (- 6)$ .

x = 2 \cdot 0.99452189

$x = 2 \cdot 0.99452189$

y = (2) \sin (- 6)

$y = (2) \sin (- 6)$

Step 4

Multiply

2

$2$ by

0.99452189

$0.99452189$ .

x = 1.98904379

$x = 1.98904379$

y = (2) \sin (- 6)

$y = (2) \sin (- 6)$

Step 5

Evaluate

\sin (- 6)

$\sin (- 6)$ .

x = 1.98904379

$x = 1.98904379$

y = 2 \cdot - 0.10452846

$y = 2 \cdot - 0.10452846$

Step 6

Multiply

2

$2$ by

- 0.10452846

$- 0.10452846$ .

x = 1.98904379

$x = 1.98904379$

y = - 0.20905692

$y = - 0.20905692$

Step 7

The rectangular representation of the polar point

(2, - 6)

$(2, - 6)$ is

(1.98904379, - 0.20905692)

$(1.98904379, - 0.20905692)$ .

(1.98904379, - 0.20905692)

$(1.98904379, - 0.20905692)$

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