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Question:

pavelpimen
pavelpimen
Student
High School - 10th Grade

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

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Posted by pavelpimen on Saturday May 30, 2009 at 7:43 AM and tagged with arccos, arcin, math, sine.

Answers:

  1. neela
    neela Teacher
    Graduate School

    eNotes Editor

    To find the value of E

    E=sin(arcsin1/2)+sin{arc[cos(sqrt3/2)]},

    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

    Therefore,E=x+y=1/2+1/2=1.

    Threfore, the value of E is 1.

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    Posted by neela on Saturday May 30, 2009 at 11:06 AM