Trigonometry Examples

$(4 \sqrt{3}, 0)$

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 $r = 4 \sqrt{3}$ and $θ = 0$ into the formulas.

$x = (4 \sqrt{3}) \cos (0)$

$y = (4 \sqrt{3}) \sin (0)$

Step 3

The exact value of $\cos (0)$ is $1$ .

$x = 4 \sqrt{3} \cdot 1$

$y = (4 \sqrt{3}) \sin (0)$

Step 4

Multiply $4$ by $1$ .

$x = 4 \sqrt{3}$

$y = (4 \sqrt{3}) \sin (0)$

Step 5

The exact value of $\sin (0)$ is $0$ .

$x = 4 \sqrt{3}$

$y = 4 \sqrt{3} \cdot 0$

Step 6

Multiply $4 \sqrt{3} \cdot 0$ .

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Step 6.1

Multiply $0$ by $4$ .

$x = 4 \sqrt{3}$

$y = 0 \sqrt{3}$

Step 6.2

Multiply $0$ by $\sqrt{3}$ .

$x = 4 \sqrt{3}$

$y = 0$

$x = 4 \sqrt{3}$

$y = 0$

Step 7

The rectangular representation of the polar point $(4 \sqrt{3}, 0)$ is $(4 \sqrt{3}, 0)$ .

$(4 \sqrt{3}, 0)$