How do you convert $r cos (\frac{x}{2}) - r sin (\frac{x}{2}) = 0$ $rcos(x/2) - rsin(x/2) = 0$ to rectangular form?

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How do you convert $r cos (\frac{x}{2}) - r sin (\frac{x}{2}) = 0$ $rcos(x/2) - rsin(x/2) = 0$ to rectangular form?

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Answer 1 · 2016-12-22T12:01:59

$x = 0$ $color(green)(x=0)$

Explanation:

I have assumed that the given equation could be better expressed as
$XXX r cos (\frac{θ}{2}) - r sin (\frac{θ}{2}) = 0$ $color(white)("XXX")r cos(theta/2)-r sin(theta/2)=0$
to avoid using $x$ $x$ which is normally associated with the rectangular form.

$\Rightarrow$ $rArr$ $color(white)("XXX")cancel(r) cos(theta/2)=cancel(r) sin(theta/2)$

$rArr$ $color(white)("XXX")theta/2 = pi/4 (color(gray)(+-kpi, k in ZZ))$

$rArr$ $color(white)("XXX")theta = pi/2 (color(gray)(+-k2pi, k in ZZ))$

Therefore we have a vertical line through the origin,
or, in terms of rectangular elements, $x=0$

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How do you convert $r cos (\frac{x}{2}) - r sin (\frac{x}{2}) = 0$ $rcos(x/2) - rsin(x/2) = 0$ to rectangular form?

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Explanation:

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How do you convert $r cos (\frac{x}{2}) - r sin (\frac{x}{2}) = 0$ $rcos(x/2) - rsin(x/2) = 0$ to rectangular form?