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Calculate E=sin(arcsin1/2)+sin{arccos [(sqrt3)/2]}.

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pavelpimen | Student, Undergraduate | (Level 3) Honors

Posted May 29, 2009 at 11:43 PM via web

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Calculate E=sin(arcsin1/2)+sin{arccos [(sqrt3)/2]}.

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neela | High School Teacher | (Level 3) Valedictorian

Posted May 30, 2009 at 3:06 AM (Answer #1)

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To find the value of E


There are two terms . We shall simplify term by term.

Firrst term sin(arcsin1/2) = x say, then by definition,

arcsin1/2 =arcsinx. by comparison, oviously x=1/2.

The second term:

We know that arccos X  = arcsin sqrt(1-X^2). Use this idea here.

sin arc(cos(sqrt3/2))=y say.

y =sin[sinarcssqrt(1-(sqrt3/2)^2)]=sqrt(1-3/4)=sqrt(1/4) =1/2

Therefore, y=1/2


Threfore, the value of E is 1.

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