How do you convert $(4, \frac{π}{6})$ $(4, pi/6)$ to rectangular form?

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How do you convert $(4, \frac{π}{6})$ $(4, pi/6)$ to rectangular form?

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Answer 1 · 2016-07-22T15:34:30

$(4, \frac{π}{6}) \to (2 \sqrt{3}, 2)$ $(4,pi/6)to(2sqrt3,2)$

Explanation:

To convert from $polar to cartesian form$ $color(blue)"polar to cartesian form"$

That is $(r, θ) \to (x, y)$ $(r,theta)to(x,y)$

$Reminder$ $color(orange)"Reminder"$

$color(red)(|bar(ul(color(white)(a/a)color(black)(x=rcostheta,y=rsintheta)color(white)(a/a)|)))$

here r = 4 and $theta=pi/6$

$color(orange)"Reminder"$

$color(red)(|bar(ul(color(white)(a/a)color(black)(cos(pi/6)=sqrt3/2" and " sin(pi/6)=1/2)color(white)(a/a)|)))$

$rArrx=4cos(pi/6)=4xxsqrt3/2=2sqrt3$ and

$y=4sin(pi/6)=4xx1/2=2$

Thus $(4,pi/6)to(2sqrt3,2)$

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How do you convert $(4, \frac{π}{6})$ $(4, pi/6)$ to rectangular form?

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Explanation:

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