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c2 trigonometrical identities and simple equestions

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    cos3q=-1 (q is the degree)
    the answers are 60, 180 and 300
    so i dont know how to solve this
    this what i did, the intervals 3*0 and 3*360=1080
    so my values are 180 , 360 , 540, 720, 900, 1080.
    cos3q=180 , 360 , 540, 720, 900, 1080
    (divide by 3)=60, 120, 180, 300, 360
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    (Original post by reb0xx)
    cos3q=-1 (q is the degree)
    the answers are 60, 180 and 300
    so i dont know how to solve this
    this what i did, the intervals 3*0 and 3*360=1080
    so my values are 180 , 360 , 540, 720, 900, 1080.
    cos3q=180 , 360 , 540, 720, 900, 1080
    (divide by 3)=60, 120, 180, 300, 360
     \displaystyle cos3q=-1

    The interval is,  \displaystyle 0\le q \le 360
    The interval for '3q' is  \displaystyle  0\le 3q \le 1080

    Solving  \displaystyle cos3q=-1 will give us 3 solutions. One solution you will get from the calculator the other two solutions can be found by adding 360 and 720 to the calculator value. Now divide the solutions by 3 to get the required values of 'q'.

    Below is the graph of y=cos(3q), this shows that it has 3 solution in the interval  \displaystyle 0\le q \le 360 .

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    (Original post by reb0xx)
    cos3q=-1 (q is the degree)
    the answers are 60, 180 and 300
    so i dont know how to solve this
    this what i did, the intervals 3*0 and 3*360=1080
    so my values are 180 , 360 , 540, 720, 900, 1080.
    cos3q=180 , 360 , 540, 720, 900, 1080
    (divide by 3)=60, 120, 180, 300, 360
    \cos 3\theta = -1 



\cos ^-1 (-1) = 180

    For the next two values, add 360 each time, as the Cosine graph repeats every
    360^{\circ} 



We have 180, (180+360), (180+360+360)

Which is; 180, 540, 900



So, 3\theta = 180, 540, 900

        \theta = 60, 180, 300

    Does this help?
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    (Original post by raheem94)
     \displaystyle cos3q=-1

    The interval is,  \displaystyle 0\le q \le 360
    The interval for '3q' is  \displaystyle  0\le 3q \le 1080

    Solving  \displaystyle cos3q=-1 will give us 3 solutions. One solution you will get from the calculator the other two solutions can be found by adding 360 and 720 to the calculator value. Now divide the solutions by 3 to get the required values of 'q'.

    Below is the graph of y=cos(3q), this shows that it has 3 solution in the interval  \displaystyle 0\le q \le 360 .

    thanks man i solved this
    but can you help me with this one
    4sinq=tanq
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    (Original post by reb0xx)
    thanks man i solved this
    but can you help me with this one
    4sinq=tanq
     \displaystyle 4sinq  = tanq

    Remember,  \displaystyle tanq=\frac{sinq}{cosq}

     \displaystyle 4sinq  = tanq \implies 4sinq=\frac{sinq}{cosq} \implies 4sinq - \frac{sinq}{cosq} =0

    Now factorise the above expression, e.g.  \displaystyle 4x -\frac{x}{y}=0 \implies x\left(4-\frac1{y}\right)=0 This gives  \displaystyle x=0 and  \displaystyle 4-\frac1{y}\right = 0
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    (Original post by raheem94)
     \displaystyle 4sinq  = tanq

    Remember,  \displaystyle tanq=\frac{sinq}{cosq}

     \displaystyle 4sinq  = tanq \implies 4sinq=\frac{sinq}{cosq} \implies 4sinq - \frac{sinq}{cosq} =0

    Now factorise the above expression, e.g.  \displaystyle 4x -\frac{x}{y}=0 \implies x\left(4-\frac1{y}\right)=0 This gives  \displaystyle x=0 and  \displaystyle 4-\frac1{y}\right = 0
    why did you chose sin to be x ?
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    (Original post by reb0xx)
    why did you chose sin to be x ?
    I was giving you an example.
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    (Original post by raheem94)
    I was giving you an example.
    ok one last question
    i can solve this equations using with the quadratic equation formula
    this one(http://www.oncalc.com/wp-content/upl...calculator.gif)
    are we allowed to solve this with a formula or by completing the square instead of factorizing it???
    are we allowed to do that in the exams?
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    (Original post by reb0xx)
    ok one last question
    i can solve this equations using with the quadratic equation formula
    this one(http://www.oncalc.com/wp-content/upl...calculator.gif)
    are we allowed to solve this with a formula or by completing the square instead of factorizing it???
    are we allowed to do that in the exams?
    Which question are you talking about?

    If the question doesn't specifies a method then you can use any method.

    In your previous question, we got,  \displaystyle 4sinq - \frac{sinq}{cosq} = 0

    Here there is no point of using any formula or completing the square, this can easily be solved by factorisation.

     \displaystyle 4sinq - \frac{sinq}{cosq} = 0 \implies sinq\left(4-\frac1{cosq}\right)=0

    So we get two equations,  \displaystyle sinq=0 and  \displaystyle 4-\frac1{cosq}=0

    Do you get it?

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Updated: April 7, 2012
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