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Math Help - Finding exact value of trig expression given sides

  1. #1
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    Finding exact value of trig expression given sides

    Hello. I am new to this forum.

    The problem is:

    Find cos (s-t) given cos s = -1/2, with s in quadrant III, and cos t = -3/5, with t in quadrant III.

    I found s = 60 deg. I am having trouble finding t though. In the triangle with angle t, -4 is the "length" of the side opposite t. So the lengths of triangle t are 3, 4, and 5. I found that out through the pythagorean theorem. I think the main thing I don't understand may be how to relate these lengths to the properties of the two special right triangles.
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  2. #2
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    Re: Finding exact value of trig expression given sides

    Quote Originally Posted by VincentPaul View Post
    Hello. I am new to this forum.

    The problem is:

    Find cos (s-t) given cos s = -1/2, with s in quadrant III, and cos t = -3/5, with t in quadrant III.

    I found s = 60 deg. I am having trouble finding t though. In the triangle with angle t, -4 is the "length" of the side opposite t. So the lengths of triangle t are 3, 4, and 5. I found that out through the pythagorean theorem. I think the main thing I don't understand may be how to relate these lengths to the properties of the two special right triangles.
    \cos{s} = -\frac{1}{2} , \sin{s} = -\frac{\sqrt{3}}{2} and, btw, s = 240^\circ

    if \cos{t} = -\frac{3}{5} , \sin{t} = -\frac{4}{5}

    \cos(s-t) = \cos{s}\cos{t} + \sin{s}\sin{t}

    plug and chug ...
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  3. #3
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    Re: Finding exact value of trig expression given sides

    Oh, I understand now. Thanks.
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