Trigonometry Examples

$(- 6, 4)$

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 $r = - 6$ and $θ = 4$ into the formulas.

$x = (- 6) \cos (4)$

$y = (- 6) \sin (4)$

Step 3

Evaluate $\cos (4)$ .

$x = - 6 \cdot 0.99756405$

$y = (- 6) \sin (4)$

Step 4

Multiply $- 6$ by $0.99756405$ .

$x = - 5.9853843$

$y = (- 6) \sin (4)$

Step 5

Evaluate $\sin (4)$ .

$x = - 5.9853843$

$y = - 6 \cdot 0.06975647$

Step 6

Multiply $- 6$ by $0.06975647$ .

$x = - 5.9853843$

$y = - 0.41853884$

Step 7

The rectangular representation of the polar point $(- 6, 4)$ is $(- 5.9853843, - 0.41853884)$ .

$(- 5.9853843, - 0.41853884)$