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Calculate arccos-1+arcsin1=?

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ruals | Salutatorian

Posted July 17, 2013 at 5:13 PM via web

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Calculate arccos-1+arcsin1=?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 17, 2013 at 5:28 PM (Answer #1)

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You should use the following trigonometric identity for an inverse trigonometric function whose argument is negative, such that:

`arc cos (-a) = pi - arc cos a`

Reasoning by analogy, yields:

`arc cos (-1) = pi - arc cos 1`

Replacing 0 for ` arc cos 1 ` and `pi/2` for `arc sin 1` yields:

`arc cos (-1) + arc sin 1 = pi - 0 + pi/2`

Bringing the terms to the right to a common denominator yields:

`arc cos (-1) + arc sin 1 = (2pi + pi)/2`

`arc cos (-1) + arc sin 1 = (3pi)/2`

Hence, evaluating `arc cos (-1) + arc sin 1` yields `arc cos (-1) + arc sin 1 = (3pi)/2` .

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