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Determine what is E=sin(arcsin1/2)+sin(arccos `sqrt3` /2)?

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ruals | Salutatorian

Posted July 17, 2013 at 5:29 PM via web

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Determine what is E=sin(arcsin1/2)+sin(arccos `sqrt3` /2)?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 17, 2013 at 5:46 PM (Answer #1)

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You should use the following relations between the trigonometric functions and inverse trigonometric functions, such that:

`sin(arcsin x) = x`

`sin(arc cos x) = sqrt(1 - x^2)`

Reasoning by analogy, yields:

`sin(arcsin (1/2)) = 1/2`

`sin(arc cos (sqrt3/2)) = sqrt(1 - (sqrt3/2)^2) => sin(arc cos (sqrt3/2)) = sqrt(1 - 3/4) => sin(arc cos (sqrt3/2)) = 1/2`

Replacing `1/2` for `sin(arcsin (1/2))`   and `1/2` for `sin(arc cos (sqrt3/2))` yields:

`E = sin(arcsin (1/2)) + sin(arc cos (sqrt3/2))`

`E = 1/2 + 1/2 => E = 1`

Hence, evaluating the value of the given expression that contains inverse trigonometric functions, yields `E = 1` .

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