How do you find the value of Csc(-8pi/6)?

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How do you find the value of Csc(-8pi/6)?

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Answer 1 · 2015-10-24T21:43:43

Find the value of $csc (- \frac{8 π}{6})$ $csc (-(8pi)/6)$

Ans: $\frac{2 \sqrt{3}}{3}$ $(2sqrt3)/3$

Explanation:

$csc (- \frac{8 π}{6}) = csc (- \frac{4 π}{3}) = \frac{1}{sin (- \frac{4 π}{3})} .$ $csc (-(8pi)/6) = csc (-(4pi)/3) = 1/sin (-(4pi)/3).$
First, find $sin (\frac{- 4 π}{3})$ $sin ((-4pi)/3)$
$sin (\frac{- 4 π}{3}) = sin (\frac{2 π}{3}) = \frac{\sqrt{3}}{2}$ $sin ((-4pi)/3) = sin ((2pi)/3) = sqrt3/2$ (co-terminal arcs).

$csc (\frac{- 4 π}{3}) = \frac{1}{sin} = \frac{2}{\sqrt{3}} = \frac{2 \sqrt{3}}{3}$ $csc ((-4pi)/3) = 1/(sin) = 2/sqrt3 = (2sqrt3)/3$

Check by calculator.
$sin (\frac{- 4 π}{3}) = sin (- 240^{\circ}) = 0.87$ $sin ((-4pi)/3) = sin (-240^@) = 0.87$
$sin (\frac{- 4 π}{3}) = \frac{\sqrt{3}}{2} = \frac{1.73}{2} = 0.87$ $sin ((-4pi)/3) = sqrt3/2 = 1.73/2 = 0.87$ . OK

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How do you find the value of Csc(-8pi/6)?

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