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Math Help - Transformations with Trig

  1. #1
    Junior Member
    Joined
    Feb 2010
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    43

    Transformations with Trig

    Hi,

    In the attached file, I do not know how to answer (a)(ii).

    I would be grateful for any help,

    Thanks.
    Attached Thumbnails Attached Thumbnails Transformations with Trig-cos.jpg  
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  2. #2
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
    Posts
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    Lightbulb here it is

    f(t)=acosb(t-c)+d
    maximum value is at t=3 but for maximum value cosb(t-c) should be maximum that is 1 therefor
    29=a+d............................................ ...1
    minimum value at t=9 but for minimum value cosb(t-c) should be minimum that is -1 therefor
    15=-a+d............................................... 2
    solving equation 1 and 2 we get
    a=7
    b=22
    now
    f(t)=7cosb(t-c)+22
    since max value was 29 at t=3 therefor
    29=7cosb(3-c)+22 or
    7=7cosb(3-c) or
    cosb(3-c)=1 or
    b(3-c)=0.................................3 (cosx=1 then x=0)
    similarly we have
    15=7cosb(9-c)+22 or
    cosb(9-c)=-1 or
    b(9-c)=pi..................................4 (cosx=-1 then x=pi)
    solving equation 3 and 4 simultaneously we get
    b=pi/6 hence proved
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