Trigonometry Examples

$(- 3, 4)$

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 $r = - 3$ and $θ = 4$ into the formulas.

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

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

Step 3

Evaluate $\cos (4)$ .

$x = - 3 \cdot 0.99756405$

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

Step 4

Multiply $- 3$ by $0.99756405$ .

$x = - 2.99269215$

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

Step 5

Evaluate $\sin (4)$ .

$x = - 2.99269215$

$y = - 3 \cdot 0.06975647$

Step 6

Multiply $- 3$ by $0.06975647$ .

$x = - 2.99269215$

$y = - 0.20926942$

Step 7

The rectangular representation of the polar point $(- 3, 4)$ is $(- 2.99269215, - 0.20926942)$ .

$(- 2.99269215, - 0.20926942)$