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Math Help - unit circle trigonometry

  1. #1
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    unit circle trigonometry

    I am totally confused on these two:

    first one: Use the unit circle to define cos theta and sin theta for any number theta between 0 and 360, inclusive. then explain how to use cos theta and sin theta to define tan theta.

    ((for this one, I knwo you can find tangent by putting sin or cos, so I assume tangent theta is sin theta or cos theta? i don't get the rest of the problem, and I don't know if i'm right on this last part.))

    second one: Show that your method in the previous question allows you to define cos theta, sin theta, and tan theta for numbers theta greater than 360 and also for numbers theta less than 0. What do you suppose it means for an angle to be negative?


    PLEASE HELP ON THESE, thank you SO MUCH anyone who doess

    edit: Also, how do I use a unit circle to find sin 240 and cos 240? is sin 16pi and cos 12 or is that totally off?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by pyrosilver View Post
    I am totally confused on these two:

    first one: Use the unit circle to define cos theta and sin theta for any number theta between 0 and 360, inclusive. then explain how to use cos theta and sin theta to define tan theta.

    ((for this one, I knwo you can find tangent by putting sin or cos, so I assume tangent theta is sin theta or cos theta? i don't get the rest of the problem, and I don't know if i'm right on this last part.))

    second one: Show that your method in the previous question allows you to define cos theta, sin theta, and tan theta for numbers theta greater than 360 and also for numbers theta less than 0. What do you suppose it means for an angle to be negative?


    PLEASE HELP ON THESE, thank you SO MUCH anyone who doess

    edit: Also, how do I use a unit circle to find sin 240 and cos 240? is sin 16pi and cos 12 or is that totally off?
    so, to first address the part in red, you should know that \tan x = \frac {\sin x}{\cos x}


    now, moving on. remember how sine and cosine are defined. they are the functions that give the points on the unit circle. that is, all points (x,y) on the circle, have the form (\cos \theta, \sin \theta), where \theta is the angle measured counter-clockwise from the positive x-axis, to the line that connects the origin with the point (x,y) = (\cos \theta , \sin \theta )

    of course, from this you can draw right-triangles and all that good stuff and derive everything you want using the trig ratios
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