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How do you convert $θ = \frac{2 π}{3}$ $theta=(2pi)/3$ into cartesian form?

1 Answer

Nov 4, 2016

$y = - \frac{1}{\sqrt{3}} x$ $y=-1/sqrt(3)x$

Explanation:

As per the diagram below using a unit circle
$color(white0("XXX") theta=(2pi)/3$

Gives a slope of $\frac{\frac{1}{2}}{- \frac{\sqrt{3}}{2}} = - \frac{1}{\sqrt{3}}$ $(1/2)/(-sqrt(3)/2)= -1/sqrt(3)$ enter image source here

Using the slope-intercept form
$XXX y = m x + b$ $color(white)("XXX")y=color(blue)mx+color(red)b$
with slope $m = - \frac{1}{\sqrt{3}}$ $color(blue)(m=-1/sqrt(3))$
and y-intercept $b = 0$ $color(red)(b=0)$

gives $y = - \frac{1}{\sqrt{3}} x + 0$ $y=color(blue)(-1/sqrt(3)x +color(red)0$

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