What are the six trig function values of $\frac{5 π}{3}$ $(5pi)/3$ ?

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What are the six trig function values of $\frac{5 π}{3}$ $(5pi)/3$ ?

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Answer 1 · 2018-05-17T00:11:25

Use trig table and unit circle -->
$sin (\frac{5 π}{3}) = sin (- \frac{π}{3} + \frac{6 π}{3}) = sin (- \frac{π}{3}) = - \frac{sin π}{3} = - \frac{\sqrt{3}}{2}$ $sin ((5pi)/3) = sin (-pi/3 + (6pi)/3) = sin (-pi/3) = - sin pi/3 = - sqrt3/2$
$cos (\frac{5 π}{3}) = cos (- \frac{π}{3} + 2 π) = cos (- \frac{π}{3}) = cos (\frac{π}{3}) = \frac{1}{2}$ $cos ((5pi)/3) = cos (-pi/3 + 2pi) = cos (-pi/3) = cos (pi/3) = 1/2$
$tan (\frac{5 π}{3}) = \frac{sin}{cos} = (\frac{\sqrt{3}}{2}) (\frac{2}{1}) = \sqrt{3}$ $tan ((5pi)/3) = sin/(cos) = (sqrt3/2)(2/1) = sqrt3$
$cot (\frac{5 π}{3}) = \frac{1}{tan} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$ $cot ((5pi)/3) = 1/(tan) = 1/sqrt3 = sqrt3/3$
$sec (\frac{5 π}{3}) = \frac{1}{cos} = 2$ $sec ((5pi)/3) = 1/(cos) = 2$
$csc (\frac{5 π}{3}) = \frac{1}{sin} = \frac{2}{\sqrt{3}} = 2 \frac{\sqrt{3}}{3}$ $csc ((5pi)/3) = 1/(sin) = 2/sqrt3 = 2sqrt3/3$

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