What does $arcsin (cos (\frac{- 2 π}{3}))$ $arcsin(cos ((-2pi)/3))$ equal?

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What does $arcsin (cos (\frac{- 2 π}{3}))$ $arcsin(cos ((-2pi)/3))$ equal?

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Answer 1 · 2016-02-26T02:25:58

$- π$ $-pi$ /6

Explanation:

cos ( $-$ $-$ 2 $π$ $pi$ /3 ) = sin ( $π$ $pi$ /2 + ( $- 2 π$ $-2pi$ /3 $)) = sin (-$ $)) = sin (-$ pi#/6)
arc sin (sin) is unit operator 1.

Answer 2 · 2016-02-26T03:27:09

(7pi)/6 and (11pi)/6

Explanation:

On the trig unit circle,
$cos (\frac{- 2 π}{3}) = = \frac{cos (2 π)}{3} = - \frac{1}{2}$ $cos ((-2pi)/3) = = cos (2pi)/3 = - 1/2$
$sin x = - \frac{1}{2}$ $sin x = -1/2$ --> arc $x = - \frac{π}{6}$ $x = - pi/6$ and $x = - \frac{5 π}{6} .$ $x = -(5pi)/6.$
Answer using positive arcs (co-terminal arcs):
$x = \frac{7 π}{6}$ $x = (7pi)/6$ and $x = \frac{11 π}{6}$ $x = (11pi)/6$

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What does $arcsin (cos (\frac{- 2 π}{3}))$ $arcsin(cos ((-2pi)/3))$ equal?

2 Answers

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Explanation:

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