How do you find all six trigonometric functions of $\frac{5 π}{6}$ $(5pi)/6$ ?

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How do you find all six trigonometric functions of $\frac{5 π}{6}$ $(5pi)/6$ ?

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Answer 1 · 2015-05-22T03:48:44

On the trig unit circle:

$sin (\frac{5 π}{6}) = sin (π - \frac{π}{6}) = sin (\frac{π}{6}) = \frac{1}{2}$ $sin ((5pi)/6) = sin (pi - pi/6) = sin (pi/6) = 1/2$

$cos (\frac{5 π}{6}) = cos (π - \frac{π}{6}) = - cos (\frac{π}{6}) = \frac{- \sqrt{3}}{2}$ $cos ((5pi)/6) = cos (pi - pi/6) = -cos (pi/6) = (-sqrt3)/2$

$tan (\frac{5 π}{6}) = \frac{1}{- \sqrt{3}} = \frac{- \sqrt{3}}{3}$ $tan ((5pi)/6) = 1/(-sqrt3) = (-sqrt3)/3$

$cot (\frac{5 π}{6}) = \frac{1}{tan (\frac{5 π}{6})}$ $cot ((5pi)/6) = 1/tan ((5pi)/6)$ =

$sec = \frac{1}{cos (\frac{5 π}{6})}$ $sec = 1/cos ((5pi)/6)$

$csc = \frac{1}{sin (\frac{5 π}{6})} =$ $csc = 1/sin ((5pi)/6) =$

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How do you find all six trigonometric functions of $\frac{5 π}{6}$ $(5pi)/6$ ?

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How do you find all six trigonometric functions of $\frac{5 π}{6}$ $(5pi)/6$ ?