How do you find the six trigonometric functions of $\frac{- π}{3}$ $(-pi)/3$ ?

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How do you find the six trigonometric functions of $\frac{- π}{3}$ $(-pi)/3$ ?

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Answer 1 · 2015-06-03T13:06:59

$\frac{π}{3}$ $pi/3$ (and by extension $\frac{- π}{3}$ $(-pi)/3$ is an angle of one of the standard trigonometric triangles:
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From this we can see
$XXXX$ $color(white)("XXXX")$ $sin (- \frac{π}{3}) = - \sqrt{\frac{3}{2}}$ $sin(-pi/3) = -sqrt(3/2)$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $csc (- \frac{π}{3}) = - \frac{2}{\sqrt{3}}$ $csc(-pi/3) = -2/sqrt(3)$

$XXXX$ $color(white)("XXXX")$ $cos (- \frac{π}{3}) = \frac{1}{2}$ $cos(-pi/3) = 1/2$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $sec (- \frac{π}{3}) = 2$ $sec(-pi/3) = 2$

$XXXX$ $color(white)("XXXX")$ $tan (- \frac{π}{3}) = - \sqrt{3}$ $tan(-pi/3) = -sqrt(3)$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ $cot (- \frac{π}{3}) = - \frac{1}{\sqrt{3}}$ $cot(-pi/3) = - 1/sqrt(3)$

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How do you find the six trigonometric functions of $\frac{- π}{3}$ $(-pi)/3$ ?

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