How do you evaluate $cot (\frac{3 π}{2})$ $cot((3pi)/2)$ ?

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How do you evaluate $cot (\frac{3 π}{2})$ $cot((3pi)/2)$ ?

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Answer 1 · 2015-05-04T03:23:52

If you consider an angle to be positioned
centered on the origin of the Cartesian plane
with a base arm along the positive X-axis
then
the terminal arm of $\frac{3 π}{2}$ $(3pi)/2$ is along the negative Y-axis.

The $cot (\frac{3 π}{2})$ $cot((3pi)/2)$ is the value of $x$ $x$ divided by the value of $y$ $y$ for any point along the terminal arm.
$x = 0$ $x=0$ for all points along the terminal arm

$cot (\frac{3 π}{2}) = 0$ $cot((3pi)/2)=0$

Answer 2 · 2015-05-05T03:50:48

$\frac{cot (3 π)}{2} = cot (\frac{π}{2} + π) = \frac{cot π}{2}$ $cot (3pi)/2 = cot(pi/2 + pi) = cot pi/2$
On the trig unit circle $cot (\frac{π}{2}) = 0, t h e n$ $cot (pi/2) = 0, then$
$cot (\frac{3 π}{2}) = 0$ $cot ((3pi)/2) = 0$

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How do you evaluate $cot (\frac{3 π}{2})$ $cot((3pi)/2)$ ?

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