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convert (5, pi/6) to rectangular coordinates

Sagot :

RedRicin
Polar coordinates are written as the distance of the point to the origin and its angle of elevation around the unit cirlce.

Draw a right triangle with an angle of [tex]\frac{\pi}6[/tex] and a hypotenuse with a length of 5.

You can use trigonometric ratios to find the legs of this triangle, which are the x and y coordinates of the point.

[tex]\cos=\frac{adj}{hyp} \\\\ \cos(\frac{\pi}6)=\frac{x}5 \\\\ \frac{\sqrt{3}}2=\frac{x}5 \\\\ \frac{5\sqrt{3}}2=x[/tex]

As for y...

[tex]\sin=\frac{opp}{hyp}\\\\\sin(\frac{\pi}6) = \frac{y}5 \\\\ \frac{1}2=\frac{y}5 \\\\ \frac{5}2=y[/tex]

[tex]\boxed{(\frac{5\sqrt{3}}2,\ \frac{5}2)}[/tex]
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