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Math Help - Please help me with this GCSE trigo question

  1. #1
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    Please help me with this GCSE trigo question

    Given that x is measured in radians and x>20, find the smallest value of x such that


    Is this an inequality question?
    Can someone please guide me how should I start with

    Thanks!!
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  2. #2
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    Quote Originally Posted by NyRychVantel View Post
    Given that x is measured in radians and x>20, find the smallest value of x such that


    Is this an inequality question?
    Can someone please guide me how should I start with

    Thanks!!
    General solution:

    \cos \left( \frac{x - 1}{3} \right) = - \frac{\sqrt{5}}{4}

    \Rightarrow \frac{x - 1}{3} = \cos^{-1} \left( - \frac{\sqrt{5}}{4}\right) + 2 n \pi or \frac{x - 1}{3} = \pi + \cos^{-1} \left(\frac{\sqrt{5}}{4}\right) + 2 n \pi where n is an integer.

    You want the smallest solution for x that is larger than 20.


    Of course, if you have access to the appropriate technology you could always use a graph to get the answer .......
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    General solution:

    \cos \left( \frac{x - 1}{3} \right) = - \frac{\sqrt{5}}{4}

    \Rightarrow \frac{x - 1}{3} = \cos^{-1} \left( - \frac{\sqrt{5}}{4}\right) + 2 n \pi or \frac{x - 1}{3} = \pi + \cos^{-1} \left(\frac{\sqrt{5}}{4}\right) + 2 n \pi where n is an integer.

    You want the smallest solution for x that is larger than 20.


    Of course, if you have access to the appropriate technology you could always use a graph to get the answer .......
    Please correct me if I'm wrong.
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  4. #4
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    Quote Originally Posted by NyRychVantel View Post
    Please correct me if I'm wrong.
    Correct (assuming accuracy to 1 decimal place is required)
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