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Trig problems

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  1. Offline

    ReputationRep:
    This is about addition formulae


    Solve the following for 0 <= x <= 2pi

    sin x = 3 cos (x - pi/6)

    ---

    This is what I did (Wrong!)


    sin x = 3 (cos x cos pi/6 + sin x sin pi/6)

    sin x = 3 cos x cos pi/6 + 3 sin x sin pi/6

    sin x - 3 sin x sin pi/6 = 3 cos x cos pi/6

    sin x (1 - 3 sin pi/6) = 3 cos x cos pi/6

    1 - 3 sin pi/6 = 3 cot x cos pi/6

    and now I'm stuck...

    help..

    Jorge
  2. Offline

    ReputationRep:
    Well, sin(pi/6) = 0.5, and cos(pi/6) = (rt3)/2

    So, that should help. From then on, it's just a matter of rearranging for cotx, and then solving.
  3. Offline

    ReputationRep:
    sinx = 3cos(x-pi/6)

    cos(x-pi/6) = cos(x)cos(pi/6) - sin(x)sin(pi/6)
    cos(x-pi/6) = cos(x)sqrt3/2 - sin(x)/2

    sinx = 3[cos(x)sqrt3/2 - sin(x)/2]
    sinx = {(3sqrt3)/2}cosx - (3/2)sinx
    5/2sinx = {(3sqrt3)/2}cosx
    tanx = {(3sqrt3)/2}/(5/2)
    tanx = {(3sqrt3)/2}.(2/5)
    tanx = {(6sqrt3)/10}
    tanx = {(3sqrt3)/5

    x = 0.805
    x = 3.95
  4. Offline

    ReputationRep:
    (Original post by El Stevo)
    sinx = 3cos(x-pi/6)

    cos(x-pi/6) = cos(x)cos(pi/6) - sin(x)sin(pi/6)
    cos(x-pi/6) = cos(x)sqrt3/2 - sin(x)/2

    sinx = 3[cos(x)sqrt3/2 - sin(x)/2]
    sinx = {(3sqrt3)/2}cosx - (3/2)sinx
    5/2sinx = {(3sqrt3)/2}cosx
    tanx = {(3sqrt3)/2}/(5/2)
    tanx = {(3sqrt3)/2}.(2/5)
    tanx = {(6sqrt3)/10}
    tanx = {(3sqrt3)/5

    x = 0.805
    x = 3.95
    cosx cos(pi/6)+sinxsin(pi/6)
  5. Offline

    ReputationRep:
    (Original post by El Stevo)
    sinx = 3cos(x-pi/6)

    cos(x-pi/6) = cos(x)cos(pi/6) - sin(x)sin(pi/6)
    cos(x-pi/6) = cos(x)sqrt3/2 - sin(x)/2

    sinx = 3[cos(x)sqrt3/2 - sin(x)/2]
    sinx = {(3sqrt3)/2}cosx - (3/2)sinx
    5/2sinx = {(3sqrt3)/2}cosx
    tanx = {(3sqrt3)/2}/(5/2)
    tanx = {(3sqrt3)/2}.(2/5)
    tanx = {(6sqrt3)/10}
    tanx = {(3sqrt3)/5

    x = 0.805
    x = 3.95
    Thanks everybody, I got it

    sinx = 3(cosx sqrt3/2 + sinx/2)

    -sinx/2 = cosx 3sqrt3/2

    sinx = - cos 3sqrt3

    tanx = - 3sqrt3 = -1.38

    between 0 and 2pi > 1.76 and 4.90

    Thanks
  6. Offline

    ReputationRep:
    (Original post by Jorge)
    Thanks everybody, I got it

    sinx = 3(cosx sqrt3/2 + sinx/2)

    -sinx/2 = cosx 3sqrt3/2

    sinx = - cos 3sqrt3

    tanx = - 3sqrt3 = -1.38

    between 0 and 2pi > 1.76 and 4.90

    Thanks
    yep same as my answer
Updated: January 15, 2005
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