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Logs and Trig Exam Question Help

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    Been doing loads of past papers for my C2 exam next week, and both of these questions I got parts of the question wrong.

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    For the first one I got:

     4(1-Cos^2\theta)=3+Cos^2\theta-1

4Cos^2\theta + Cos^2\theta-1=0

    And I factorised using the quadratic formula to get:
    \theta= 67, 293, 130, 230

    But this is wrong...



    For the second one I got n=2.71 through the use of simultaneous equations. I then substituted in n to find a value for a. I got 8.99 which is way out of the mark scheme's tolerance.

    Any help will be appreciated. I can post exactly what I did if it will help, just let me know.

    Thanks,
    Sora
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    (Original post by Sora)
    Been doing loads of past papers for my C2 exam next week, and both of these questions I got parts of the question wrong.

    Click image for larger version. 

Name:	logs-trig.png 
Views:	29 
Size:	27.5 KB 
ID:	147120

    For the first one I got:

     4(1-Cos^2\theta)=3+Cos^2\theta-1

4Cos^2\theta + Cos^2\theta-1=0

    And I factorised using the quadratic formula to get:
    \theta= 67, 293, 130, 230

    But this is wrong...



    For the second one I got n=2.71 through the use of simultaneous equations. I then substituted in n to find a value for a. I got 8.99 which is way out of the mark scheme's tolerance.

    Any help will be appreciated. I can post exactly what I did if it will help, just let me know.

    Thanks,
    Sora
    Why the hell did you used the quadratic formula?

     \displaystyle 4cos^2 \theta + cos^2\theta -1=0 \implies 5cos^2\theta = 1 \implies cos^2\theta = \frac15 \implies cos\theta = \pm \sqrt{\frac15}

    Now solve it.
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    I can't read my own writing xD Thank you!

    Any help on the logs?
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    (Original post by Sora)
    I can't read my own writing xD Thank you!

    Any help on the logs?
     y = ax^n

    Sub in (2,6),  6=a 2^n \longrightarrow (1)

    Sub in (3,18),  18=a3^n \longrightarrow (2)

    Now divide (2) by (1), and then use logs.
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    Both of these were silly mistakes on my part -.- Thank you

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