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Write an Algebraic Expression equivalent to (cos(arcsin(2x)). watch

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    So I'm taking Geometry and Pre-Calculus next year, and i'm in need of help with this one problem on my Pre-Calc packet for the summer. I'm so angry because it's the only problem out of a 21 page booklet that i can't get. here it is...

    Write an algebraic expression equivalent to cos(arcsin(2x)).

    i've got a few ideas of how to start, but i'm just not getting anywhere. any help, even just the first step or two to get me going, would be helpful!
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    so let's say arcsin(2x) = the angle A

    you draw a right-angled triangle and call one of the non-90 angles A and you wanna find cosA and you know two of the sides already...

    you ok from here?
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    hintage. write is as cos(arcsin(2x))=y then square.


    Answer, only for checking when you've done it yourself
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    \displaystyle \sqrt{1-4x^2}
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    i'm thinking i sort of am half way there-ish. a bit more help would be great. that or i can just wait until tomorrow when it isn't the middle of the night, ha that might help too.
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    god i swear we learned this this year i don't know how i'm confused by this.
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    (Original post by Rocious)
    so let's say arcsin(2x) = the angle A

    you draw a right-angled triangle and call one of the non-90 angles A and you wanna find cosA and you know two of the sides already...

    you ok from here?



    mk i lied, you might have to walk me through it. ha sorry
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    oh wait. snap i think i got it.
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    (Original post by Anick14)
    mk i lied, you might have to walk me through it. ha sorry
    have you tried my hint?

    the trick with Rocious's hint is that if you know that one of the angles is arcsin(2x), let the hypotenuse=1 then what do you know...
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    yeah i got it. it should have made total sense after the first post, but i got it now.

    then you use the pythagorean theorem to solve for the adjacent side which'll end up being what you said. ha my apologies guys, at least now i'll probably never forget it.
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    (Original post by Totally Tom)
    hintage. write is as cos(arcsin(2x))=y then square.


    Answer, only for checking when you've done it yourself
    Spoiler:
    Show
    \displaystyle \sqrt{1-4x^2}

    I figured this fairly quickly using the hint above , it's a bit of an unusual question but not too bad.

    A further hint , note that sin(arcsin(p)) = p , this should tell you what you need to do next.

    Edit - didn't know you got it anyways
 
 
 
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