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    so this is the question:

    determine a general expression for all angles that satisfy:

    a) sin theta = 1/2

    b) tan theta = - root 3

    c) cos theta = -1

    d) sin theta = -1

    but what has confused me is that it says:

    note: solve first for -2pi < theta < 2pi, then consider how the above functions behave for other angles outside the rage.


    I'm really confused, any help would be appreciated.
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    (Original post by doctor_2_be)
    so this is the question:

    determine a general expression for all angles that satisfy:

    a) sin theta = 1/2

    b) tan theta = - root 3

    c) cos theta = -1

    d) sin theta = -1

    but what has confused me is that it says:

    note: solve first for -2pi < theta < 2pi, then consider how the above functions behave for other angles outside the rage.


    I'm really confused, any help would be appreciated.
    Here is a hint for a) but if you get the idea behind that you will know how to do the rest of the q's.

    Consider that sin(pi/6)=1/2 so pi/6 is one such angle that you will need to be able to describe. Now plot the graph of y=sin(x) over a decent interval (-2pi,2pi) perhaps like your question suggests. Now think about the symmetry of the sin function. What other angles can you deduce have a sin of 1/2 in this interval? And how can you describe all the other angles that have this as well? Once you have figured it out over the small interval it should be fairly straight forward as the sin function is periodic.

    Good luck.
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    (Original post by poorform)
    Here is a hint for a) but if you get the idea behind that you will know how to do the rest of the q's.

    Consider that sin(pi/6)=1/2 so pi/6 is one such angle that you will need to be able to describe. Now plot the graph of y=sin(x) over a decent interval (-2pi,2pi) perhaps like your question suggests. Now think about the symmetry of the sin function. What other angles can you deduce have a sin of 1/2 in this interval? And how can you describe all the other angles that have this as well? Once you have figured it out over the small interval it should be fairly straight forward as the sin function is periodic.

    Good luck.
    So for sin(x)=-1 would it be:

    (2pi)n - ( pi/2) & (2pi)n + (3pi/2)
 
 
 
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