Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Trig problems

Announcements Posted on
Talking about ISA/EMPA specifics is against our guidelines - read more here 05-03-2015
  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
2015 general election
New on TSR

Loved by Students

Our big survey results unveiled

Article updates
Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.