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Math Help - finding solutions for cos

  1. #1
    Junior Member madmax29's Avatar
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    finding solutions for cos

    I have to find the two solutions for;

     <br />
cos(2t)=-0.75, \pi < t < 2 \pi<br />

    i have sketched a graph, but am unsure how to get the values mathematically?

    Many thanks
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  2. #2
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    Quote Originally Posted by madmax29 View Post
    I have to find the two solutions for;

     <br />
cos(2t)=-0.75, \pi < t < 2 \pi<br />
    \pi < t < 2\pi

    2\pi < 2t < 4\pi

    \cos(2t) = -0.75


    2t = 2\pi + \arccos(-0.75)

    t = \pi + \frac{1}{2}\arccos(-0.75)


    2t = 4\pi - \arccos(-0.75)

    t = 2\pi - \frac{1}{2}\arccos(-0.75)
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  3. #3
    Junior Member madmax29's Avatar
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    the question then goes on to say, "if the solutions are denoted by t1 and t2 where t1 < t2, find t1 and t2?"

    what are the answers?
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  4. #4
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    Quote Originally Posted by madmax29 View Post
    the question then goes on to say, "if the solutions are denoted by t1 and t2 where t1 < t2, find t1 and t2?"

    what are the answers?
    you can't tell which solution for t is the largest or smallest?
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  5. #5
    Junior Member madmax29's Avatar
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    is it 8.70 rads & 10.15 rads, or 4.35 rads & 5.07 rads????
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  6. #6
    Junior Member madmax29's Avatar
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    Quote Originally Posted by skeeter View Post
    you can't tell which solution for t is the largest or smallest?
    i can, but i need to know which range, both seems to satisfy the t1 < t2 criteria??? but which is which, if you see what i mean?
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  7. #7
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    one more time ...

    t = \pi + \frac{1}{2}\arccos(-0.75)

    t = 2\pi - \frac{1}{2}\arccos(-0.75)

    evaluate each value of t in your calculator ... check the results with your graph.
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  8. #8
    Junior Member madmax29's Avatar
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    so because the summary of the statement is a just a t as apposed to 2t, then the ones with t are the real answers? would this statement be correct?
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  9. #9
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    Quote Originally Posted by madmax29 View Post
    so because the summary of the statement is a just a t as apposed to 2t, then the ones with t are the real answers? would this statement be correct?
    The answer has been given - twice. You are asked to solve for t.
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