Question

determine the cartesian coordinates for a point that has the polar coordinates ( r = 5.30 , \text{m} ) and ( \theta = 160^circ ).
( x = ) (\text{m})
( y = ) (\text{m})
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Explanation:

Step1: Calculate x-coordinate

Use $x = r\cos\theta$
$x = 5.30 \times \cos(160^\circ)$
$x = 5.30 \times (-0.9397) \approx -4.98$

Step2: Calculate y-coordinate

Use $y = r\sin\theta$
$y = 5.30 \times \sin(160^\circ)$
$y = 5.30 \times 0.3420 \approx 1.81$

Answer:

$x = -4.98$ m, $y = 1.81$ m