Trigonometry Examples

$(2, - p)$

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 $r = 2$ and $θ = - p$ into the formulas.

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

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

Step 3

Since $\cos (- p)$ is an even function, rewrite $\cos (- p)$ as $\cos (p)$ .

$x = 2 \cos (p)$

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

Step 4

Since $\sin (- p)$ is an odd function, rewrite $\sin (- p)$ as $- \sin (p)$ .

$x = 2 \cos (p)$

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

Step 5

Multiply $- 1$ by $2$ .

$x = 2 \cos (p)$

$y = - 2 \sin (p)$

Step 6

The rectangular representation of the polar point $(2, - p)$ is $(2 \cos (p), - 2 \sin (p))$ .

$(2 \cos (p), - 2 \sin (p))$