Trigonometry Examples

$(- \sqrt{3}, - 1)$

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 $r = - \sqrt{3}$ and $θ = - 1$ into the formulas.

$x = (- \sqrt{3}) \cos (- 1)$

$y = (- \sqrt{3}) \sin (- 1)$

Step 3

Evaluate $\cos (- 1)$ .

$x = - \sqrt{3} \cdot 0.99984769$

$y = (- \sqrt{3}) \sin (- 1)$

Step 4

Multiply $- \sqrt{3} \cdot 0.99984769$ .

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Step 4.1

Multiply $0.99984769$ by $- 1$ .

$x = - 0.99984769 \sqrt{3}$

$y = (- \sqrt{3}) \sin (- 1)$

Step 4.2

Multiply $- 0.99984769$ by $\sqrt{3}$ .

$x = - 1.731787$

$y = (- \sqrt{3}) \sin (- 1)$

$x = - 1.731787$

$y = (- \sqrt{3}) \sin (- 1)$

Step 5

Evaluate $\sin (- 1)$ .

$x = - 1.731787$

$y = - \sqrt{3} \cdot - 0.0174524$

Step 6

Multiply $- \sqrt{3} \cdot - 0.0174524$ .

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Step 6.1

Multiply $- 0.0174524$ by $- 1$ .

$x = - 1.731787$

$y = 0.0174524 \sqrt{3}$

Step 6.2

Multiply $0.0174524$ by $\sqrt{3}$ .

$x = - 1.731787$

$y = 0.03022845$

$x = - 1.731787$

$y = 0.03022845$

Step 7

The rectangular representation of the polar point $(- \sqrt{3}, - 1)$ is $(- 1.731787, 0.03022845)$ .

$(- 1.731787, 0.03022845)$