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    Hi guys, would anyone know how to answer this question:

    Given that:

    y = arccos x

    -1<(or equal to) x < (or equal to) 1

    0 < (or equal to) y < (or equal to) pi


    a) express arcsin x in terms of y


    So far I have x = cos y, but the mark scheme then writes:

    x = sin(pi/2 -y)

    arcsin x = pi/2 -y

    Any help'd be great
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    What didn't you understand?

    Did you know \cos y = \sin (\frac{\pi}{2}-y) ?

    The graphs of y=sin x and y=cos x are translations of each other.

    Draw a right angled triangle and call one angle y, one pi/2 and the other (pi/2 - y). Try to see why this identity is true.

    Alternatively use the expansion of sin(A - B).
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    I understand that cos x = sin(x + pi/2)

    because the cos graph is the sine graph moved pi/2 to the left (I think), but I can't see how sin(pi/2 - y) relates in the same way sorry
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    (Original post by sinkersub)
    I understand that cos x = sin(x + pi/2)

    because the cos graph is the sine graph moved pi/2 to the left (I think), but I can't see how sin(pi/2 - y) relates in the same way sorry
    Well I have shown you two methods but here's a third.

    \sin \theta =\sin(\pi - \theta)

    Let \theta = x + \frac{\pi}{2}
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    I think I got it, but roughly,

    Is it ok to look at the graphs or arccos and arcsin individually, and the fact that arcsin up by pi/2 and flipped in the y axis gives the same translation?
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    (Original post by sinkersub)
    I think I got it, but roughly,

    Is it ok to look at the graphs or arccos and arcsin individually, and the fact that arcsin up by pi/2 and flipped in the y axis gives the same translation?
    That's fine but you must use the proper language of transformations. Up? Flipped?
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    yeah with that in mind , but I'll ask about it when we go back, thanks anyway
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    (Original post by sinkersub)
    I think I got it, but roughly,

    Is it ok to look at the graphs or arccos and arcsin individually, and the fact that arcsin up by pi/2 and flipped in the y axis gives the same translation?
    This is a 1 mark question

    You are expected to know that arcsinx + arccosx = pi/2
 
 
 
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