Trigonometry Examples

(- 3, 4)

$(- 3, 4)$

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 = - 3

$r = - 3$ and

θ = 4

$θ = 4$ into the formulas.

x = (- 3) cos (4)

$x = (- 3) \cos (4)$

y = (- 3) sin (4)

$y = (- 3) \sin (4)$

Step 3

Evaluate

cos (4)

$\cos (4)$ .

x = - 3 \cdot 0.99756405

$x = - 3 \cdot 0.99756405$

y = (- 3) sin (4)

$y = (- 3) \sin (4)$

Step 4

Multiply

- 3

$- 3$ by

0.99756405

$0.99756405$ .

x = - 2.99269215

$x = - 2.99269215$

y = (- 3) sin (4)

$y = (- 3) \sin (4)$

Step 5

Evaluate

sin (4)

$\sin (4)$ .

x = - 2.99269215

$x = - 2.99269215$

y = - 3 \cdot 0.06975647

$y = - 3 \cdot 0.06975647$

Step 6

Multiply

- 3

$- 3$ by

0.06975647

$0.06975647$ .

x = - 2.99269215

$x = - 2.99269215$

y = - 0.20926942

$y = - 0.20926942$

Step 7

The rectangular representation of the polar point

(- 3, 4)

$(- 3, 4)$ is

(- 2.99269215, - 0.20926942)

$(- 2.99269215, - 0.20926942)$ .

(- 2.99269215, - 0.20926942)

$(- 2.99269215, - 0.20926942)$