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    When drawing a graph for instance of
    cos(theta - 45 degrees) why is everything shifted to the right and not to the left -? - missing something basic here me thinks

    cheers
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    You learned this when you studied graph transformations.

    The graph of y=f(x-k) is a translation of y=f(x) by k units in the positive x direction.
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    Thanks, I need to go and manually draw some graphs then - cheers
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    (Original post by Blackcat99)
    When drawing a graph for instance of
    cos(theta - 45 degrees) why is everything shifted to the right and not to the left -? - missing something basic here me thinks

    cheers
    The theta - 45 degrees results in the argument (i.e. the number in the bracket which the cosine function actually acts on) being 45 degrees smaller than "normal". This may sound obvious and, in a way, it is.

    However, this means that, if our initial input is x, the cosine function acts on (x-45) and so the output of the entire, composite function when the initial input value is x is the output of the cosine function for (x-45).

    So we get the "height" of x-45 "normally" at x instead of at x-45. Hence the graph effectively shifts 45 to the RIGHT as x is 45 bigger than x-45.

    I hope this helps, it may initially seem counter-intuitive.
 
 
 
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