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    find the values of x in the range 0degrees < or equal to x < or equal 360 degrees. that satisfy sec(2x)=3

    no idea what to do :/
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    (Original post by iamgreatness)
    find the values of x in the range 0degrees < or equal to x < or equal 360 degrees. that satisfy sec(2x)-3

    no idea what to do :/
    sec(2x)-3 is an expression and expressions don't have solutions.

    You've missed something out of your question.
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    (Original post by notnek)
    sec(2x)-3 is an expression and expressions don't have solutions.

    You've missed something out of your question.
    im sorry its =3
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    (Original post by iamgreatness)
    find the values of x in the range 0degrees < or equal to x < or equal 360 degrees. that satisfy sec(2x)=3

    no idea what to do :/
    \displaystyle \sec 2x = \frac{1}{\cos 2x}

    so you can manipulate the equation to give

    \displaystyle \cos 2x = \frac{1}{3}

    Can you continue from here? If not, post your working/ideas.
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    (Original post by notnek)
    \displaystyle \sec 2x = \frac{1}{\cos 2x}

    so you can manipulate the equation to give

    \displaystyle \cos 2x = \frac{1}{3}

    Can you continue from here? If not, post your working/ideas.
    i cant do it
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    (Original post by iamgreatness)
    i cant do it
    You don't know how to solve the equation \displaystyle \cos 2x = \frac{1}{3} between 0 and 360 degrees?

    Could you solve \displaystyle \cos u = \frac{1}{3} between 0 and 720 degrees?

    If so make a substitution u = 2x.
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    (Original post by iamgreatness)
    i cant do it
    How would you solve \displaystyle \cos x =\frac{1}{3}?

    Do the same for this but here you'll have '2x =' intead of 'x ='.

    Again, post any working and any ideas that you have if you're still stuck. This is not a solutions forum and it's hard to help if I don't know your problem.
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    (Original post by Mr M)
    You don't know how to solve the equation \cos 2x = 3 between 0 and 360 degrees?

    Could you solve \cos u = 3 between 0 and 720 degrees?

    If so make a substitution u = 2x.
    \cos 2x = 3 or \cos u = 3 have no solution

    because  -1 \leq \cos (anything) \leq 1
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    (Original post by ztibor)
    ...
    Well yes, we both know that was a typo.
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    (Original post by notnek)
    How would you solve \displaystyle \cos x =\frac{1}{3}?

    Do the same for this but here you'll have '2x =' intead of 'x ='.

    Again, post any working and any ideas that you have if you're still stuck. This is not a solutions forum and it's hard to help if I don't know your problem.
    (Original post by Mr M)
    You don't know how to solve the equation \displaystyle \cos 2x = \frac{1}{3} between 0 and 360 degrees?

    Could you solve \displaystyle \cos u = \frac{1}{3} between 0 and 720 degrees?

    If so make a substitution u = 2x.
    im sorry i cant do it

    what bit is this whats it called i will look it up in my textbook but does it have a name e.g partial fracitons
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    (Original post by iamgreatness)
    im sorry i cant do it

    what bit is this whats it called i will look it up in my textbook but does it have a name e.g partial fracitons
    This is just Core 2 trigonometry. You really should know it inside out by the time you study Core 4.
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    (Original post by iamgreatness)
    find the values of x in the range 0degrees < or equal to x < or equal 360 degrees. that satisfy sec(2x)=3

    no idea what to do :/
    sec(2x) = 3

    => 1/cos(2x) = 3

    => cos(2x) = 1/3

    Name:  Opgave cos.jpg
Views: 52
Size:  32.3 KBclick to magnify

    Coordinate system contains the graphs of cos(2x) and 1/3, you can see they meet 4 times in the interval 0 to 360 degrees. So you are looking for 4 solutions.

    Now use the inverse cosine (cos-1) function on your calculator to find one of the solutions.

    Solution 1
    cos-1(1/3) = 70.529 degrees

    2x = 70.529 degrees

    x = 35.264 degrees

    Solution 2
    Because of symmetri on the graph, solution 2 must be 180 degrees minus solution 1, solution 3 is 180 plus solution 1 and solution 4 is 360 minus solution1. (Use unit-circle to clarify this to yourself if coordinatsystem doesn't make sense)

    x = 180 - 35.264 = 144.736 degrees

    Solution 3

    x = 180 + 35.264 = 215.264 degrees

    Solution 4

    x = 360 - 35.264 = 324.736 degrees
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    (Original post by Mr M)
    This is just Core 2 trigonometry. You really should know it inside out by the time you study Core 4.
    i got a B in c2, duno why this is in c4 section A examples then
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    (Original post by Studentdk)
    ...
    Full solutions are not allowed in this forum. Please read the posting guide before making another post.
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    (Original post by iamgreatness)
    i got a B in c2, duno why this is in c4 section A examples then
    Because of the use of the reciprocal trigonometric ratio.
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    (Original post by iamgreatness)
    i got a B in c2, duno why this is in c4 section A examples then
    Do you understand what to do now?

    I don't believe that you had literally no idea how to solve \cos x = \frac{1}{3} in that region.

    To find one solution would be a GCSE question.
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    (Original post by notnek)
    Do you understand what to do now?

    I don't believe that you had literally no idea how to solve \cos x = \frac{1}{3} in that region.

    To find one solution would be a GCSE question.
    => 1/cos(2x) = 3

    => cos(2x) = 1/3

    it was just this step i had trouble with. i guess u just flip over the 1/cox(2x) to get cos2x and coz u flipped that u have to flip the 3 which makes 1/3??
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    (Original post by Studentdk)
    sec(2x) = 3

    => 1/cos(2x) = 3

    => cos(2x) = 1/3

    Name:  Opgave cos.jpg
Views: 52
Size:  32.3 KBclick to magnify

    Coordinate system contains the graphs of cos(2x) and 1/3, you can see they meet 4 times in the interval 0 to 360 degrees. So you are looking for 4 solutions.

    Now use the inverse cosine (cos-1) function on your calculator to find one of the solutions.

    Solution 1
    cos-1(1/3) = 70.529 degrees

    2x = 70.529 degrees

    x = 35.264 degrees

    Solution 2
    Because of symmetri on the graph, solution 2 must be 180 degrees minus solution 1, solution 3 is 180 plus solution 1 and solution 4 is 360 minus solution1. (Use unit-circle to clarify this to yourself if coordinatsystem doesn't make sense)

    x = 180 - 35.264 = 144.736 degrees

    Solution 3

    x = 180 + 35.264 = 215.264 degrees

    Solution 4

    x = 360 - 35.264 = 324.736 degrees
    thnx altho ur not supposed to post full solutions sometimes, like arnold scwarzeneger said, u have to bend rules. thank u
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    (Original post by notnek)
    Full solutions are not allowed in this forum. Please read the posting guide before making another post.
    I apologise for having gone against the common spirit of this forum by posting a full solution, I was not aware of this "rule".

    I do however believe that the person asking the question had received so many hints without understanding, that at some point the best help would be to see a solution.
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    (Original post by iamgreatness)
    => 1/cos(2x) = 3

    => cos(2x) = 1/3

    it was just this step i had trouble with. i guess u just flip over the 1/cox(2x) to get cos2x and coz u flipped that u have to flip the 3 which makes 1/3??
    You should have mentioned this before.

    \displaystyle \frac{1}{\cos 2x} = 3 \implies 1=3\cos 2x \implies \cos 2x = \frac{1}{3}
 
 
 
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